The thesis examines efficient Bayesian marginal likelihood estimation in generalized linear latent variable models. It compares joint and marginal Monte Carlo estimators for estimating the Bayesian marginal likelihood. The marginal estimators have lower Monte Carlo error than the joint estimators due to differences in the variables being averaged. The thesis also explores using the Metropolis kernel to marginalize out latent variables, which allows estimating the marginal likelihood without sampling the full joint parameter space.
This document discusses different methods for obtaining p-values when assessing the fit of latent class models, including asymptotic, bootstrap, and posterior predictive p-values. It describes latent class analysis and common test statistics used to evaluate model fit, such as the likelihood ratio statistic and Pearson chi-squared statistic. The document then provides an overview of how asymptotic, bootstrap, and posterior predictive p-values are calculated. Specifically, it explains that asymptotic p-values assume the proposed model is true, while bootstrap and posterior predictive p-values generate empirical reference distributions through resampling techniques. The purpose is to compare these p-value methods in assessing latent class model fit under different sample sizes.
1) Canonical correlation analysis (CCA) is a statistical method that analyzes the correlation relationship between two sets of multidimensional variables.
2) CCA finds linear transformations of the two sets of variables so that their correlation is maximized. This can be formulated as a generalized eigenvalue problem.
3) The number of dimensions of the transformed variables is determined using Bartlett's test, which tests the eigenvalues against a chi-squared distribution.
A comparative study of clustering and biclustering of microarray dataijcsit
There are subsets of genes that have similar behavior under subsets of conditions, so we say that they
coexpress, but behave independently under other subsets of conditions. Discovering such coexpressions can
be helpful to uncover genomic knowledge such as gene networks or gene interactions. That is why, it is of
utmost importance to make a simultaneous clustering of genes and conditions to identify clusters of genes
that are coexpressed under clusters of conditions. This type of clustering is called biclustering.
Biclustering is an NP-hard problem. Consequently, heuristic algorithms are typically used to approximate
this problem by finding suboptimal solutions. In this paper, we make a new survey on clustering and
biclustering of gene expression data, also called microarray data.
A Survey of String Matching AlgorithmsIJERA Editor
The concept of string matching algorithms are playing an important role of string algorithms in finding a place where one or several strings (patterns) are found in a large body of text (e.g., data streaming, a sentence, a paragraph, a book, etc.). Its application covers a wide range, including intrusion detection Systems (IDS) in computer networks, applications in bioinformatics, detecting plagiarism, information security, pattern recognition, document matching and text mining. In this paper we present a short survey for well-known and recent updated and hybrid string matching algorithms. These algorithms can be divided into two major categories, known as exact string matching and approximate string matching. The string matching classification criteria was selected to highlight important features of matching strategies, in order to identify challenges and vulnerabilities.
This document presents a novel approach for measuring shape similarity and using it for object recognition. The key steps are:
1) Solving the correspondence problem between two shapes by attaching a descriptor called "shape context" to sample points on each shape. Shape context captures the distribution of remaining points relative to the reference point.
2) Using the point correspondences to estimate an aligning transformation between the shapes. This provides a measure of shape similarity as the matching error between corresponding points plus the magnitude of the transformation.
3) Treating recognition as a nearest neighbor problem to find the most similar stored prototype shape. The approach is demonstrated on various datasets including handwritten digits, silhouettes, and 3D objects
Dependency analysis is a technique to detect dependencies between tasks that prevent these tasks from running in parallel. It is an important aspect of parallel programming tools. Dependency analysis techniques are used to determine how much of the code is parallelizable. Literature shows that number of data dependence test has been proposed for parallelizing loops in case of arrays with linear subscripts, however less work has been done for arrays with nonlinear subscripts. GCD test, Banerjee method, Omega test, I-test dependence decision algorithms are used for one-dimensional arrays under constant or variable bounds. However, these approaches perform well only for nested loop with linear array subscripts. The Quadratic programming (QP) test, polynomial variable interval (PVI) test, Range test are typical techniques for nonlinear subscripts. The paper presents survey of these different data dependence analysis tests.
This document discusses how AI can help advance various scientific fields such as mathematics, quantum chemistry, biology, and more. It provides examples of how machine learning has helped mathematicians develop new theories by analyzing patterns in examples. It also discusses how AI is helping push the limits of density functional theory in quantum chemistry and how AlphaFold uses transformers and protein multiple sequence alignments to predict structures with near experimental accuracy. The conclusion emphasizes not becoming a slave to models and maintaining inspiration.
There are subsets of genes that have similar behavior under subsets of conditions, so we say
that they coexpress, but behave independently under other subsets of conditions. Discovering
such coexpressions can be helpful to uncover genomic knowledge such as gene networks or
gene interactions. That is why, it is of utmost importance to make a simultaneous clustering of
genes and conditions to identify clusters of genes that are coexpressed under clusters of
conditions. This type of clustering is called biclustering.
Biclustering is an NP-hard problem. Consequently, heuristic algorithms are typically used to
approximate this problem by finding suboptimal solutions. In this paper, we make a new survey
on biclustering of gene expression data, also called microarray data.
This document discusses different methods for obtaining p-values when assessing the fit of latent class models, including asymptotic, bootstrap, and posterior predictive p-values. It describes latent class analysis and common test statistics used to evaluate model fit, such as the likelihood ratio statistic and Pearson chi-squared statistic. The document then provides an overview of how asymptotic, bootstrap, and posterior predictive p-values are calculated. Specifically, it explains that asymptotic p-values assume the proposed model is true, while bootstrap and posterior predictive p-values generate empirical reference distributions through resampling techniques. The purpose is to compare these p-value methods in assessing latent class model fit under different sample sizes.
1) Canonical correlation analysis (CCA) is a statistical method that analyzes the correlation relationship between two sets of multidimensional variables.
2) CCA finds linear transformations of the two sets of variables so that their correlation is maximized. This can be formulated as a generalized eigenvalue problem.
3) The number of dimensions of the transformed variables is determined using Bartlett's test, which tests the eigenvalues against a chi-squared distribution.
A comparative study of clustering and biclustering of microarray dataijcsit
There are subsets of genes that have similar behavior under subsets of conditions, so we say that they
coexpress, but behave independently under other subsets of conditions. Discovering such coexpressions can
be helpful to uncover genomic knowledge such as gene networks or gene interactions. That is why, it is of
utmost importance to make a simultaneous clustering of genes and conditions to identify clusters of genes
that are coexpressed under clusters of conditions. This type of clustering is called biclustering.
Biclustering is an NP-hard problem. Consequently, heuristic algorithms are typically used to approximate
this problem by finding suboptimal solutions. In this paper, we make a new survey on clustering and
biclustering of gene expression data, also called microarray data.
A Survey of String Matching AlgorithmsIJERA Editor
The concept of string matching algorithms are playing an important role of string algorithms in finding a place where one or several strings (patterns) are found in a large body of text (e.g., data streaming, a sentence, a paragraph, a book, etc.). Its application covers a wide range, including intrusion detection Systems (IDS) in computer networks, applications in bioinformatics, detecting plagiarism, information security, pattern recognition, document matching and text mining. In this paper we present a short survey for well-known and recent updated and hybrid string matching algorithms. These algorithms can be divided into two major categories, known as exact string matching and approximate string matching. The string matching classification criteria was selected to highlight important features of matching strategies, in order to identify challenges and vulnerabilities.
This document presents a novel approach for measuring shape similarity and using it for object recognition. The key steps are:
1) Solving the correspondence problem between two shapes by attaching a descriptor called "shape context" to sample points on each shape. Shape context captures the distribution of remaining points relative to the reference point.
2) Using the point correspondences to estimate an aligning transformation between the shapes. This provides a measure of shape similarity as the matching error between corresponding points plus the magnitude of the transformation.
3) Treating recognition as a nearest neighbor problem to find the most similar stored prototype shape. The approach is demonstrated on various datasets including handwritten digits, silhouettes, and 3D objects
Dependency analysis is a technique to detect dependencies between tasks that prevent these tasks from running in parallel. It is an important aspect of parallel programming tools. Dependency analysis techniques are used to determine how much of the code is parallelizable. Literature shows that number of data dependence test has been proposed for parallelizing loops in case of arrays with linear subscripts, however less work has been done for arrays with nonlinear subscripts. GCD test, Banerjee method, Omega test, I-test dependence decision algorithms are used for one-dimensional arrays under constant or variable bounds. However, these approaches perform well only for nested loop with linear array subscripts. The Quadratic programming (QP) test, polynomial variable interval (PVI) test, Range test are typical techniques for nonlinear subscripts. The paper presents survey of these different data dependence analysis tests.
This document discusses how AI can help advance various scientific fields such as mathematics, quantum chemistry, biology, and more. It provides examples of how machine learning has helped mathematicians develop new theories by analyzing patterns in examples. It also discusses how AI is helping push the limits of density functional theory in quantum chemistry and how AlphaFold uses transformers and protein multiple sequence alignments to predict structures with near experimental accuracy. The conclusion emphasizes not becoming a slave to models and maintaining inspiration.
There are subsets of genes that have similar behavior under subsets of conditions, so we say
that they coexpress, but behave independently under other subsets of conditions. Discovering
such coexpressions can be helpful to uncover genomic knowledge such as gene networks or
gene interactions. That is why, it is of utmost importance to make a simultaneous clustering of
genes and conditions to identify clusters of genes that are coexpressed under clusters of
conditions. This type of clustering is called biclustering.
Biclustering is an NP-hard problem. Consequently, heuristic algorithms are typically used to
approximate this problem by finding suboptimal solutions. In this paper, we make a new survey
on biclustering of gene expression data, also called microarray data.
Final generalized linear modeling by idrees waris iugcId'rees Waris
This document discusses generalized linear models (GLM). It begins by introducing the topic and outlines the main points to be covered, including the history of GLM, assumptions for using GLM, and how to run GLM in SPSS. The document then covers the components of GLM, including the random, systematic, and link components. It discusses various distributions and link functions that can be used in GLM. The document concludes by providing an example of how to analyze shipping damage incident data using Poisson GLM in SPSS.
: “Generalized Linear Models” is an online course offered at Statistics.com. Statistics.com is the leading provider of online education in statistics, and offers over 100 courses in introductory and advanced statistics. Courses typically are taught by leading experts. Some course highlights -
A. Taught by renowned International Faculty (Not self-paced learning)
B. Instructor led and Peer learning
C. Flexible and Convenient schedule
D. Practical Application and Software skills
For more details please contact info@c-elt.com.
Website: www.india.statistics.com
1) The document presents an approach to solving the inverse kinematics problem of robotic manipulators using genetic algorithms.
2) Genetic algorithms are applied by encoding joint angles into chromosomes and evaluating fitness based on end-effector position and orientation accuracy.
3) The approach handles redundancies and singularities effectively and can compute motions for manipulators to follow specified end-effector paths.
This paper proposes using fuzzy cognitive maps (FCM) to automatically detect a student's learning style in an adaptive e-learning system based on the Felder-Silverman learning style model. FCM is a soft computing technique that combines fuzzy logic and neural networks. The paper reviews related work on automatic detection of learning styles. It then explains how FCM would be used to model student behaviors and interactions to identify their learning style dimensions. The results of testing this approach are discussed. The overall goal is to personalize the e-learning experience based on a student's detected learning style.
GENERATING SUMMARIES USING SENTENCE COMPRESSION AND STATISTICAL MEASURESijnlc
The document summarizes a technique for generating summaries using sentence compression and statistical measures. It first implements a graph-based technique to achieve sentence compression and information fusion. It then uses hand-crafted syntactic rules to prune compressed sentences. Finally, it uses probabilistic measures and word co-occurrence to obtain the summaries. The system can generate summaries at any user-defined compression rate.
Structural Dynamic Reanalysis of Beam Elements Using Regression MethodIOSR Journals
This paper concerns with the reanalysis of Structural modification of a beam element based on
natural frequencies using polynomial regression method. This method deals with the characteristics of
frequency of a vibrating system and the procedures that are available for the modification of physical
parameters of vibrating structural system. The method is applied on a simple cantilever beam structure and Tstructure
for approximate structural dynamic reanalysis. Results obtained from the assumed conditions of the
problem indicates the high quality approximation of natural frequencies using finite element method and
regression method.
Increasing interpreting needs a more objective and automatic measurement. We hold a basic idea that 'translating means translating meaning' in that we can assessment interpretation quality by comparing the
meaning of the interpreting output with the source input. That is, a translation unit of a 'chunk' named
Frame which comes from frame semantics and its components named Frame Elements (FEs) which comes
from Frame Net are proposed to explore their matching rate between target and source texts. A case study in this paper verifies the usability of semi-automatic graded semantic-scoring measurement for human
simultaneous interpreting and shows how to use frame and FE matches to score. Experiments results show that the semantic-scoring metrics have a significantly correlation coefficient with human judgment.
The document provides a literature review of different clustering techniques. It begins by defining clustering and its applications. It then categorizes and describes several clustering methods including hierarchical (BIRCH, CURE, CHAMELEON), partitioning (k-means, k-medoids), density-based (DBSCAN, OPTICS, DENCLUE), grid-based (CLIQUE, STING, MAFIA), and model-based (RBMN, SOM) methods. For each method, it discusses the algorithm, advantages, disadvantages and time complexity. The document aims to provide an overview of various clustering techniques for classification and comparison.
Use of eigenvalues and eigenvectors to analyze bipartivity of network graphscsandit
This paper presents the applications of Eigenvalues and Eigenvectors (as part of spectral
decomposition) to analyze the bipartivity index of graphs as well as to predict the set of vertices
that will constitute the two partitions of graphs that are truly bipartite and those that are close
to being bipartite. Though the largest eigenvalue and the corresponding eigenvector (called the
principal eigenvalue and principal eigenvector) are typically used in the spectral analysis of
network graphs, we show that the smallest eigenvalue and the smallest eigenvector (called the
bipartite eigenvalue and the bipartite eigenvector) could be used to predict the bipartite
partitions of network graphs. For each of the predictions, we hypothesize an expected partition
for the input graph and compare that with the predicted partitions. We also analyze the impact
of the number of frustrated edges (edges connecting the vertices within a partition) and their
location across the two partitions on the bipartivity index. We observe that for a given number
of frustrated edges, if the frustrated edges are located in the larger of the two partitions of the
bipartite graph (rather than the smaller of the two partitions or equally distributed across the
two partitions), the bipartivity index is likely to be relatively larger.
This document summarizes key concepts from Chapter 5 of the book "Pattern Recognition and Machine Learning" regarding neural networks.
1. Neural networks can overcome the curse of dimensionality by using nonlinear activation functions between layers. Common activation functions include sigmoid, tanh, and ReLU.
2. A feedforward neural network consists of an input layer, hidden layers with nonlinear activations, and an output layer. The network learns by adjusting weights in a process called backpropagation.
3. Bayesian neural networks treat the network weights as distributions and integrate them out to make predictions, avoiding overfitting. However, the posterior distribution cannot be expressed in closed form due to the nonlinear nature of neural networks.
Capital market applications of neural networks etc23tino
The document provides an overview of capital market applications of neural networks, fuzzy logic, and genetic algorithms that have been studied in academic literature. It reviews studies that use these techniques for market forecasting, trading rules, option pricing, bond ratings, and portfolio construction. For market forecasting specifically, several studies are described that use neural networks and neuro-fuzzy systems to predict stock market indexes and interest rates, finding they often outperform traditional econometric models.
FUZZY CONTROL OF A SERVOMECHANISM: PRACTICAL APPROACH USING MAMDANI AND TAKAG...ijfls
The main objective of this work is to propose two fuzzy controllers: one based on the Mamdani inference
method and another controller based on the Takagi- Sugeno inference method, both will be designed for
application in a position control system of a servomechanism. Some comparations between the methods
mentioned above will be made with regard to the performance of the system in order to identify the
advantages of the Takagi- Sugeno method in relation to the Mamdani method in the presence of
disturbances and nonlinearities of the system. Some results of simulation and practical application are
presented and results obtained showed that controllers based on Takagi- Sugeno method is more efficient
than controllers based on Mamdani method for this specific application.
This document discusses patterns for modeling object life cycles and implementing state-based behavior in objects. It describes the Objects for States pattern, which allows an object to change its behavior based on internal state by delegating state-based behavior to separate objects. It then discusses two approaches for implementing the state-based behavior objects: Stateful Object, where the behavior object has access to the context object's state; and Stateless Object, where the context object passes itself as a parameter on method calls. The document provides examples to illustrate these patterns.
Novel algorithms for detection of unknown chemical molecules with specific bi...Aboul Ella Hassanien
The document proposes novel algorithms for detecting unknown chemical molecules with specific biological activities. It introduces two approaches: 1) a qualitative structure-activity relationships approach using molecular descriptors and machine learning models, and 2) a graph algorithms based approach using a new coding system and kernel functions. For the latter, it presents a new atoms similarity algorithm and paths of stars algorithm, applying them to drug activity prediction tasks with competitive accuracy compared to other methods. The algorithms aim to reduce the time and cost of classifying chemical compounds.
Presentation summarizes main content of Farrelly, C. M. (2017). Extensions of Morse-Smale Regression with Application to Actuarial Science. arXiv preprint arXiv:1708.05712.
Paper was accepted December 2017 by Casualty Actuarial Society.
1. The document discusses mixture models and the Expectation-Maximization (EM) algorithm. It covers K-means clustering, Gaussian mixture models, and applying EM to estimate parameters for these models.
2. EM is a general technique for finding maximum likelihood solutions for probabilistic models with latent variables. It works by iteratively computing expectations of the latent variables given current parameter estimates (E-step) and maximizing the likelihood function with respect to the parameters (M-step).
3. This process is guaranteed to increase the likelihood at each iteration until convergence. EM can be applied to problems like Gaussian mixtures, Bernoulli mixtures, and Bayesian linear regression by treating certain variables as latent.
Islamic University Pattern Recognition & Neural Network 2019 Rakibul Hasan Pranto
The document discusses various topics related to pattern recognition including:
1. Pattern recognition is the automated recognition of patterns and regularities in data through techniques like machine learning. It has applications in areas like optical character recognition, diagnosis systems, and security.
2. There are two main approaches to pattern recognition - sub-symbolic and symbolic. Sub-symbolic uses connectionist models like neural networks while symbolic uses formal structures like strings and automata to represent patterns.
3. A pattern recognition system consists of steps like data acquisition, pre-processing, feature extraction, model learning, classification, and post-processing to classify patterns. Bayesian decision making and Bayes' theorem are statistical techniques used in classification.
Hybrid Method HVS-MRMR for Variable Selection in Multilayer Artificial Neural...IJECEIAES
The variable selection is an important technique the reducing dimensionality of data frequently used in data preprocessing for performing data mining. This paper presents a new variable selection algorithm uses the heuristic variable selection (HVS) and Minimum Redundancy Maximum Relevance (MRMR). We enhance the HVS method for variab le selection by incorporating (MRMR) filter. Our algorithm is based on wrapper approach using multi-layer perceptron. We called this algorithm a HVS-MRMR Wrapper for variables selection. The relevance of a set of variables is measured by a convex combination of the relevance given by HVS criterion and the MRMR criterion. This approach selects new relevant variables; we evaluate the performance of HVS-MRMR on eight benchmark classification problems. The experimental results show that HVS-MRMR selected a less number of variables with high classification accuracy compared to MRMR and HVS and without variables selection on most datasets. HVS-MRMR can be applied to various classification problems that require high classification accuracy.
This document summarizes key concepts from Chapter 8 of the book "Pattern Recognition and Machine Learning" regarding probabilistic graphical models. It introduces directed and undirected graphical models as visualization tools for probabilistic relationships between random variables. It provides examples of Bayesian networks and conditional independence. Key points covered include using graphs to factorize joint probabilities, the d-separation criteria for identifying conditional independence based on a graph, and applying these concepts to linear Gaussian models and discrete variable models.
This chapter discusses classification methods including linear discriminant functions and probabilistic generative and discriminative models. It covers linear decision boundaries, perceptrons, Fisher's linear discriminant, logistic regression, and the use of sigmoid and softmax activation functions. The key points are:
1) Classification involves dividing the input space into decision regions using linear or nonlinear boundaries.
2) Perceptrons and Fisher's linear discriminant find linear decision boundaries by updating weights to minimize misclassification.
3) Generative models like naive Bayes estimate joint probabilities while discriminative models like logistic regression directly model posterior probabilities.
4) Sigmoid and softmax functions are used to transform linear outputs into probabilities for binary and multiclass classification respectively.
An Overview of ROC Curves in SAS PROC LOGISTICQuanticate
The repeated dosing of some drugs can induce injury to the human liver. Regular monitoring of biomarkers assayed in blood samples may help to diagnose safety issues sooner. There is interest in developing new biomarkers that are more specific than the standard tests [e.g. Alanine Transaminase (ALT)] commonly used.
In medical diagnostics, a receiver operating characteristic (ROC) analysis is a powerful statistical analysis tool that is used to assess the ability of a test to correctly classify diseased (sensitivity) and non-diseased (specificity) subjects. The sensitivity and specificity rates are used to construct the ROC curve which is used to visually inspect the ability of the test to discriminate between patients’ true status of disease. The most widely used summary statistic is the area under the ROC curve (AUROC).
We present recent enhancements to PROC LOGISTIC for constructing ROC curves and compare AUROCs between biomarkers with standard errors and 95% confidence intervals (CIs). We present an overview of the code, output and interpretation of the ROC features of PROC LOGISTIC in SAS v9.3 using simulated data on two candidate biomarkers. We discuss the limitations of ROC analysis in the context of identifying and validating the best candidate biomarker.
This document provides an overview of quantitative methods topics including time value of money, discounted cash flow applications, probability concepts, and statistical measures. Key points discussed include calculating present and future value of cash flows using timelines and interest rates, as well as methods for analyzing investments like net present value, internal rate of return, and holding period return. Common statistical concepts are also summarized such as measures of central tendency, frequency distributions, and histograms.
Final generalized linear modeling by idrees waris iugcId'rees Waris
This document discusses generalized linear models (GLM). It begins by introducing the topic and outlines the main points to be covered, including the history of GLM, assumptions for using GLM, and how to run GLM in SPSS. The document then covers the components of GLM, including the random, systematic, and link components. It discusses various distributions and link functions that can be used in GLM. The document concludes by providing an example of how to analyze shipping damage incident data using Poisson GLM in SPSS.
: “Generalized Linear Models” is an online course offered at Statistics.com. Statistics.com is the leading provider of online education in statistics, and offers over 100 courses in introductory and advanced statistics. Courses typically are taught by leading experts. Some course highlights -
A. Taught by renowned International Faculty (Not self-paced learning)
B. Instructor led and Peer learning
C. Flexible and Convenient schedule
D. Practical Application and Software skills
For more details please contact info@c-elt.com.
Website: www.india.statistics.com
1) The document presents an approach to solving the inverse kinematics problem of robotic manipulators using genetic algorithms.
2) Genetic algorithms are applied by encoding joint angles into chromosomes and evaluating fitness based on end-effector position and orientation accuracy.
3) The approach handles redundancies and singularities effectively and can compute motions for manipulators to follow specified end-effector paths.
This paper proposes using fuzzy cognitive maps (FCM) to automatically detect a student's learning style in an adaptive e-learning system based on the Felder-Silverman learning style model. FCM is a soft computing technique that combines fuzzy logic and neural networks. The paper reviews related work on automatic detection of learning styles. It then explains how FCM would be used to model student behaviors and interactions to identify their learning style dimensions. The results of testing this approach are discussed. The overall goal is to personalize the e-learning experience based on a student's detected learning style.
GENERATING SUMMARIES USING SENTENCE COMPRESSION AND STATISTICAL MEASURESijnlc
The document summarizes a technique for generating summaries using sentence compression and statistical measures. It first implements a graph-based technique to achieve sentence compression and information fusion. It then uses hand-crafted syntactic rules to prune compressed sentences. Finally, it uses probabilistic measures and word co-occurrence to obtain the summaries. The system can generate summaries at any user-defined compression rate.
Structural Dynamic Reanalysis of Beam Elements Using Regression MethodIOSR Journals
This paper concerns with the reanalysis of Structural modification of a beam element based on
natural frequencies using polynomial regression method. This method deals with the characteristics of
frequency of a vibrating system and the procedures that are available for the modification of physical
parameters of vibrating structural system. The method is applied on a simple cantilever beam structure and Tstructure
for approximate structural dynamic reanalysis. Results obtained from the assumed conditions of the
problem indicates the high quality approximation of natural frequencies using finite element method and
regression method.
Increasing interpreting needs a more objective and automatic measurement. We hold a basic idea that 'translating means translating meaning' in that we can assessment interpretation quality by comparing the
meaning of the interpreting output with the source input. That is, a translation unit of a 'chunk' named
Frame which comes from frame semantics and its components named Frame Elements (FEs) which comes
from Frame Net are proposed to explore their matching rate between target and source texts. A case study in this paper verifies the usability of semi-automatic graded semantic-scoring measurement for human
simultaneous interpreting and shows how to use frame and FE matches to score. Experiments results show that the semantic-scoring metrics have a significantly correlation coefficient with human judgment.
The document provides a literature review of different clustering techniques. It begins by defining clustering and its applications. It then categorizes and describes several clustering methods including hierarchical (BIRCH, CURE, CHAMELEON), partitioning (k-means, k-medoids), density-based (DBSCAN, OPTICS, DENCLUE), grid-based (CLIQUE, STING, MAFIA), and model-based (RBMN, SOM) methods. For each method, it discusses the algorithm, advantages, disadvantages and time complexity. The document aims to provide an overview of various clustering techniques for classification and comparison.
Use of eigenvalues and eigenvectors to analyze bipartivity of network graphscsandit
This paper presents the applications of Eigenvalues and Eigenvectors (as part of spectral
decomposition) to analyze the bipartivity index of graphs as well as to predict the set of vertices
that will constitute the two partitions of graphs that are truly bipartite and those that are close
to being bipartite. Though the largest eigenvalue and the corresponding eigenvector (called the
principal eigenvalue and principal eigenvector) are typically used in the spectral analysis of
network graphs, we show that the smallest eigenvalue and the smallest eigenvector (called the
bipartite eigenvalue and the bipartite eigenvector) could be used to predict the bipartite
partitions of network graphs. For each of the predictions, we hypothesize an expected partition
for the input graph and compare that with the predicted partitions. We also analyze the impact
of the number of frustrated edges (edges connecting the vertices within a partition) and their
location across the two partitions on the bipartivity index. We observe that for a given number
of frustrated edges, if the frustrated edges are located in the larger of the two partitions of the
bipartite graph (rather than the smaller of the two partitions or equally distributed across the
two partitions), the bipartivity index is likely to be relatively larger.
This document summarizes key concepts from Chapter 5 of the book "Pattern Recognition and Machine Learning" regarding neural networks.
1. Neural networks can overcome the curse of dimensionality by using nonlinear activation functions between layers. Common activation functions include sigmoid, tanh, and ReLU.
2. A feedforward neural network consists of an input layer, hidden layers with nonlinear activations, and an output layer. The network learns by adjusting weights in a process called backpropagation.
3. Bayesian neural networks treat the network weights as distributions and integrate them out to make predictions, avoiding overfitting. However, the posterior distribution cannot be expressed in closed form due to the nonlinear nature of neural networks.
Capital market applications of neural networks etc23tino
The document provides an overview of capital market applications of neural networks, fuzzy logic, and genetic algorithms that have been studied in academic literature. It reviews studies that use these techniques for market forecasting, trading rules, option pricing, bond ratings, and portfolio construction. For market forecasting specifically, several studies are described that use neural networks and neuro-fuzzy systems to predict stock market indexes and interest rates, finding they often outperform traditional econometric models.
FUZZY CONTROL OF A SERVOMECHANISM: PRACTICAL APPROACH USING MAMDANI AND TAKAG...ijfls
The main objective of this work is to propose two fuzzy controllers: one based on the Mamdani inference
method and another controller based on the Takagi- Sugeno inference method, both will be designed for
application in a position control system of a servomechanism. Some comparations between the methods
mentioned above will be made with regard to the performance of the system in order to identify the
advantages of the Takagi- Sugeno method in relation to the Mamdani method in the presence of
disturbances and nonlinearities of the system. Some results of simulation and practical application are
presented and results obtained showed that controllers based on Takagi- Sugeno method is more efficient
than controllers based on Mamdani method for this specific application.
This document discusses patterns for modeling object life cycles and implementing state-based behavior in objects. It describes the Objects for States pattern, which allows an object to change its behavior based on internal state by delegating state-based behavior to separate objects. It then discusses two approaches for implementing the state-based behavior objects: Stateful Object, where the behavior object has access to the context object's state; and Stateless Object, where the context object passes itself as a parameter on method calls. The document provides examples to illustrate these patterns.
Novel algorithms for detection of unknown chemical molecules with specific bi...Aboul Ella Hassanien
The document proposes novel algorithms for detecting unknown chemical molecules with specific biological activities. It introduces two approaches: 1) a qualitative structure-activity relationships approach using molecular descriptors and machine learning models, and 2) a graph algorithms based approach using a new coding system and kernel functions. For the latter, it presents a new atoms similarity algorithm and paths of stars algorithm, applying them to drug activity prediction tasks with competitive accuracy compared to other methods. The algorithms aim to reduce the time and cost of classifying chemical compounds.
Presentation summarizes main content of Farrelly, C. M. (2017). Extensions of Morse-Smale Regression with Application to Actuarial Science. arXiv preprint arXiv:1708.05712.
Paper was accepted December 2017 by Casualty Actuarial Society.
1. The document discusses mixture models and the Expectation-Maximization (EM) algorithm. It covers K-means clustering, Gaussian mixture models, and applying EM to estimate parameters for these models.
2. EM is a general technique for finding maximum likelihood solutions for probabilistic models with latent variables. It works by iteratively computing expectations of the latent variables given current parameter estimates (E-step) and maximizing the likelihood function with respect to the parameters (M-step).
3. This process is guaranteed to increase the likelihood at each iteration until convergence. EM can be applied to problems like Gaussian mixtures, Bernoulli mixtures, and Bayesian linear regression by treating certain variables as latent.
Islamic University Pattern Recognition & Neural Network 2019 Rakibul Hasan Pranto
The document discusses various topics related to pattern recognition including:
1. Pattern recognition is the automated recognition of patterns and regularities in data through techniques like machine learning. It has applications in areas like optical character recognition, diagnosis systems, and security.
2. There are two main approaches to pattern recognition - sub-symbolic and symbolic. Sub-symbolic uses connectionist models like neural networks while symbolic uses formal structures like strings and automata to represent patterns.
3. A pattern recognition system consists of steps like data acquisition, pre-processing, feature extraction, model learning, classification, and post-processing to classify patterns. Bayesian decision making and Bayes' theorem are statistical techniques used in classification.
Hybrid Method HVS-MRMR for Variable Selection in Multilayer Artificial Neural...IJECEIAES
The variable selection is an important technique the reducing dimensionality of data frequently used in data preprocessing for performing data mining. This paper presents a new variable selection algorithm uses the heuristic variable selection (HVS) and Minimum Redundancy Maximum Relevance (MRMR). We enhance the HVS method for variab le selection by incorporating (MRMR) filter. Our algorithm is based on wrapper approach using multi-layer perceptron. We called this algorithm a HVS-MRMR Wrapper for variables selection. The relevance of a set of variables is measured by a convex combination of the relevance given by HVS criterion and the MRMR criterion. This approach selects new relevant variables; we evaluate the performance of HVS-MRMR on eight benchmark classification problems. The experimental results show that HVS-MRMR selected a less number of variables with high classification accuracy compared to MRMR and HVS and without variables selection on most datasets. HVS-MRMR can be applied to various classification problems that require high classification accuracy.
This document summarizes key concepts from Chapter 8 of the book "Pattern Recognition and Machine Learning" regarding probabilistic graphical models. It introduces directed and undirected graphical models as visualization tools for probabilistic relationships between random variables. It provides examples of Bayesian networks and conditional independence. Key points covered include using graphs to factorize joint probabilities, the d-separation criteria for identifying conditional independence based on a graph, and applying these concepts to linear Gaussian models and discrete variable models.
This chapter discusses classification methods including linear discriminant functions and probabilistic generative and discriminative models. It covers linear decision boundaries, perceptrons, Fisher's linear discriminant, logistic regression, and the use of sigmoid and softmax activation functions. The key points are:
1) Classification involves dividing the input space into decision regions using linear or nonlinear boundaries.
2) Perceptrons and Fisher's linear discriminant find linear decision boundaries by updating weights to minimize misclassification.
3) Generative models like naive Bayes estimate joint probabilities while discriminative models like logistic regression directly model posterior probabilities.
4) Sigmoid and softmax functions are used to transform linear outputs into probabilities for binary and multiclass classification respectively.
An Overview of ROC Curves in SAS PROC LOGISTICQuanticate
The repeated dosing of some drugs can induce injury to the human liver. Regular monitoring of biomarkers assayed in blood samples may help to diagnose safety issues sooner. There is interest in developing new biomarkers that are more specific than the standard tests [e.g. Alanine Transaminase (ALT)] commonly used.
In medical diagnostics, a receiver operating characteristic (ROC) analysis is a powerful statistical analysis tool that is used to assess the ability of a test to correctly classify diseased (sensitivity) and non-diseased (specificity) subjects. The sensitivity and specificity rates are used to construct the ROC curve which is used to visually inspect the ability of the test to discriminate between patients’ true status of disease. The most widely used summary statistic is the area under the ROC curve (AUROC).
We present recent enhancements to PROC LOGISTIC for constructing ROC curves and compare AUROCs between biomarkers with standard errors and 95% confidence intervals (CIs). We present an overview of the code, output and interpretation of the ROC features of PROC LOGISTIC in SAS v9.3 using simulated data on two candidate biomarkers. We discuss the limitations of ROC analysis in the context of identifying and validating the best candidate biomarker.
This document provides an overview of quantitative methods topics including time value of money, discounted cash flow applications, probability concepts, and statistical measures. Key points discussed include calculating present and future value of cash flows using timelines and interest rates, as well as methods for analyzing investments like net present value, internal rate of return, and holding period return. Common statistical concepts are also summarized such as measures of central tendency, frequency distributions, and histograms.
MLPI Lecture 2: Monte Carlo Methods (Basics)Dahua Lin
This lecture covers the basics of Monte Carlo methods, including Monte Carlo integration, Transform sampling, Rejection sampling, Importance sampling, Markov chain theory, and Markov Chain Monte Carlo (MCMC).
The Anderson–Darling test is a statistical test of whether a given sample of data is drawn from a given probability distribution. In its basic form, the test assumes that there are no parameters to be estimated in the distribution being tested, in which case the test and its set of critical values is distribution-free.
This is an implementation of Research paper titled -
Spectrum Sensing in Cognitive Radio Using Goodness of Fit Testing by Wang, Yang, Zhao and Zhang
Variance reduction techniques (VRTs) can increase the statistical efficiency of simulations by reducing the variances of random variable outputs without changing their expectations, allowing for greater precision with less simulation time. Common VRTs include common random numbers, antithetic variates, control variates, indirect estimation, and conditioning. Common random numbers are used when comparing alternative system configurations, while antithetic variates induce negative correlation between separate simulation runs to offset observations. Control variates take advantage of correlations between random variables, and indirect estimation and conditioning substitute exact analytical solutions for estimates in queueing models.
DV Analytics and SAS Training in BangaloreDV Analytics
Data Analytics Training
Course Overview
SAS Base
SAS Advanced:
Basic Data handling & Analytics
Advanced Analytics and Predictive Modeling
Excel & VBA
Access & SQL
Tableau
Qlikview
Data Analysis projects
Resume preparation and Interview support
This document introduces classification using linear models and discriminant functions. It discusses:
1) Representing binary and multi-class labels using coding schemes like 1-of-K.
2) Using a generalized linear model framework to map linear discriminant functions to class labels.
3) Solving classification problems using least squares to determine the parameters of linear discriminant functions that minimize error on training data.
However, least squares solutions for classification have deficiencies since discriminant function outputs are unconstrained and not probabilistic.
Improving Effeciency with Options in SASguest2160992
Learning
Base SAS,
Advanced SAS,
Proc SQl,
ODS,
SAS in financial industry,
Clinical trials,
SAS Macros,
SAS BI,
SAS on Unix,
SAS on Mainframe,
SAS interview Questions and Answers,
SAS Tips and Techniques,
SAS Resources,
SAS Certification questions...
visit http://sastechies.blogspot.com
This document provides an example of running an R script from Excel to create plots. It describes setting up an Excel file with buttons to run an R script and open the resulting PDF. The R script generates random data, plots it, and saves the plots to a PDF. Clicking the first button runs the R script, passing cell values as arguments. Clicking the second button opens the PDF if it was created.
ROC curves are used to evaluate machine learning algorithms and visualize the tradeoff between true positives and false positives. An ROC curve plots the true positive rate against the false positive rate for different discrimination thresholds. The area under the ROC curve (AUC) provides a single measure of performance, with higher values indicating better classification. While ROC curves are commonly used, precision-recall curves may provide a better evaluation for some applications by focusing on precision and recall rather than false positives.
Quantitative method intro variable_levels_measurementKeiko Ono
This document discusses variables, levels of measurement, and key terms in quantitative methods. It defines a variable as a property of an observation that can take on two or more values. There are three levels of measurement for variables: nominal, ordinal, and interval. Nominal variables categorize without order, ordinal can be ordered but differences are not exact, and interval variables have exact differences represented by each value. Appropriate summary statistics depend on the level of measurement, with nominal only allowing frequency and mode, ordinal adding median and range, and interval permitting all including mean, variance, minimum, and maximum.
The document provides an introduction to the R programming language. It discusses that R is an open-source programming language for statistical analysis and graphics. It can run on Windows, Unix and MacOS. The document then covers downloading and installing R and R Studio, the R workspace, basics of R syntax like naming conventions and assignments, working with data in R including importing, exporting and creating calculated fields, using R packages and functions, and resources for R help and tutorials.
This document provides an introduction to big data and Hadoop. It discusses the three V's of big data: volume, variety, and velocity. Examples are given of the large amounts of data generated daily from various sources. The growth and market opportunity for big data technologies is also discussed. Common use cases for big data in different industries are outlined. The document then covers Hadoop components and how Hadoop HDFS and MapReduce work. Other Hadoop technologies like Hive, Pig, and Zookeeper are introduced. Benefits of Hadoop and commercial Hadoop distributions are summarized. Finally, technologies alternative to Hadoop like HPCC and SAP HANA are briefly described.
The document provides answers to common questions asked in SAS interviews or for SAS certification. Key points:
- The OUTPUT statement overrides automatic output in DATA steps and writes observations only when executed.
- The STOP statement stops processing the current DATA step and resumes after.
- DROP= in the SET statement drops variables from processing, while DROP= in the DATA statement drops them from the output dataset.
- The END= option reads the last observation of a dataset to a new dataset.
This document discusses preparing data for analysis. It covers the need for data exploration including validation, sanitization, and treatment of missing values and outliers. The main steps in statistical data analysis are also presented. Specific techniques discussed include calculating frequency counts and descriptive statistics to understand the distribution and characteristics of variables in a loan data set with 250,000 observations. SAS procedures like Proc Freq, Proc Univariate, and Proc Means are demonstrated for exploring the data.
Here are the steps to solve this problem:
1) The mean (μ) of birth weights is 7.5 lbs
2) The standard deviation (σ) is 1.2 lbs
3) We want to find the probability that a randomly selected birth weight is between 6.5 and 8 lbs.
4) To calculate this, we first convert the bounds to z-scores:
z1 = (6.5 - 7.5) / 1.2 = -1
z2 = (8 - 7.5) / 1.2 = 0.5
5) Then we calculate the probability between the z-scores using the normal CDF:
P(z1 < Z < z2)
How to read a receiver operating characteritic (ROC) curveSamir Haffar
1) The document discusses how to evaluate the accuracy of diagnostic tests using receiver operating characteristic (ROC) curves.
2) ROC curves plot the sensitivity of a test on the y-axis against 1-specificity on the x-axis. The area under the ROC curve (AUC) provides an overall measure of a test's accuracy, with higher values indicating better accuracy.
3) The document uses ferritin testing to diagnose iron deficiency anemia (IDA) in the elderly as a case example. The AUC for ferritin was found to be 0.91, indicating it is an excellent test for diagnosing IDA.
This document provides data from judges' ratings of essays and colors of packaging. It calculates the coefficient of concordance (W) for the data and tests the significance.
For the essay data, W is calculated to be 0.62, indicating a moderate agreement among judges.
For the packaging color data, the null hypothesis of no significant agreement is tested against the alternative of significant agreement using a chi-squared test. The calculated chi-squared value of 21.7 exceeds the critical value of 14.07, so the null hypothesis is rejected. This indicates a considerable and significant agreement among judges in ranking the package colors.
A researcher in attempting to run a regression model noticed a neg.docxevonnehoggarth79783
A researcher in attempting to run a regression model noticed a negative beta sign for an explanatory variable when s/he was expecting a positive sign based on theoretical considerations. What advice would you give to the researcher as to what is going on and what specific diagnostics would you look at? Explain conceptually and statisticallythe different ways you cancorrect for this problem.
Reason
One of the most common and important reasons for such situations is the existence of multicollinearity. Multicollinearity can happen if some of the independent variables are highly correlated to each other or to another variable that is not in the model.
Multicollinearity also has other symptoms such as
· Large variance for regression coefficients
· Non-significant individual coefficients while the general model is significant
· Change of marginal contributions depending on the variables in the model
· Large correlation coefficients in the correlation matrix of variables
It should however be noted that the general model can preserve its predictive ability and it is only the explanatory power that is lost
Before going to the solutions and measures the researcher can take it is wise to take a step back and see the underlying reason for the multicollinearity. An extreme case where two variables are identical gives the best understanding of problem
In this case we are trying to define y as a function of and while in reality . Therefore any linear combination of and is replaceable by infinite other linear combinations (ie )
It is simply understandable that while the y is predicted correctly in all the instances individual coefficients for and are meaningless.
Diagnosis
One of the most common diagnoses for multicollinearity is the variance inflation factor (VIF)
Where
And is the coefficient of multiple determination of regression of on other variables
The variance inflation factor therefore determines how much the variance of each coefficient inflates. when equals zero VIF equals 1 which suggests zero multicollinearity heuristic is that any value of VIF larger than 10 is alerting and a case of strong multicollinearity exists.
Solution
s
There are a few solutions for the multi Collinearity problem:
1- Ignoring the problem completely is possible for cases where we only care about the final model fit and prediction capability rather than individual coefficients and explanation power
2- Removing some of the correlated variables from the model, this can be justified since we can argue the effect of variable is however seen by similar highly correlated variables that are kept in the model
3- Principle component analysis (or any orthogonal transformation) can reduce the number of factors to a few orthogonal factors with no collinearity; however we should note that the interpretation of variables after a PC transformation is hard.
4- For cases where we intend to keep all the variables in the model without any major transformation, the Ridge regr.
Regression, multivariate analysis, clustering, and predictive modeling techniques are statistical and machine learning methods for analyzing data. Regression finds relationships between variables, multivariate analysis examines multiple variables simultaneously, clustering groups similar data points, and predictive modeling predicts unknown events. These techniques are used across many fields for tasks like prediction, classification, pattern recognition, and decision making. R software can be used to perform various data analyses using these methods.
Data Analysis: Statistical Methods: Regression modelling, Multivariate Analysis - Classification: SVM & Kernel Methods - Rule Mining - Cluster Analysis, Types of Data in Cluster Analysis, Partitioning Methods, Hierarchical Methods, Density Based Methods, Grid Based Methods, Model Based Clustering Methods, Clustering High Dimensional Data - Predictive Analytics – Data analysis using R.
Regression, multivariate analysis, clustering, and predictive modeling techniques are statistical and machine learning methods for analyzing data. Regression finds relationships between variables, multivariate analysis examines multiple variables simultaneously, clustering groups similar observations, and predictive modeling predicts unknown events. These techniques are used across many fields to discover patterns, reduce dimensions, classify data, and forecast trends. R software can be used to perform various analyses including regression, clustering, and predictive modeling.
Samplying in Factored Dynamic Systems_Fadel.pdfFadel Adoe
This paper investigates modeling complex dynamic systems using dynamic Bayesian networks (DBNs) and performing inference using particle filtering. DBNs compactly represent large discrete and continuous systems using a prior over initial states and transition models. Particle filtering approximates the belief state over time as particles. It was tested on large DBNs modeling freeway traffic and a two-tank process, showing it can track states in complex systems, though it suffers from dimensionality issues. The paper proposes combining sampling with exact inference and exploiting weak interactions to better model real-world hybrid systems.
This document discusses two categories of multiscale modeling methods: parallel and concurrent multiscale modeling. Parallel modeling separates calculations at different scales and passes results between scales, while concurrent modeling solves problems simultaneously across scales. The document then proposes using concurrent multiscale modeling to estimate deformation in a CFRP/MFC composite under loading. It involves defining micro- and macroscale models, homogenizing a representative volume element at the microscale, and inputting homogenized properties into a finite element analysis at the macroscale.
This document proposes generalized additive models (GAMs) to model conditional dependence structures between random variables. Specifically, it develops a GAM framework where a dependence or concordance measure between two variables is modeled as a parametric, non-parametric, or semi-parametric function of explanatory variables. It derives the root-n consistency and asymptotic normality of the maximum penalized log-likelihood estimator for the proposed GAMs. It also discusses details of the estimation procedure and selection of smoothing parameters.
This Presentation is on recommended system on question paper predication using machine learning techniques. We did literature survey and implement using same technique.
EVALUATING SYMMETRIC INFORMATION GAP BETWEEN DYNAMICAL SYSTEMS USING PARTICLE...Zac Darcy
This paper presents a new method for evaluating the symmetric information gap between two dynamical systems using particle filters. It first describes a symmetric version of the information gap metric based on symmetric Kullback-Leibler divergence. A numerical method is then developed to approximate this symmetric K-L rate using particle filters. This represents the posterior densities of the dynamical systems as mixtures of Gaussians. The method is demonstrated on a nonlinear target tracking example, computing the symmetric information gap between two systems at each time step.
Ragui Assaad- University of Minnesota
Caroline Krafft- ST. Catherine University
ERF Training on Applied Micro-Econometrics and Public Policy Evaluation
Cairo, Egypt July 25-27, 2016
www.erf.org.eg
The document discusses probabilistic and statistical models for outlier detection, specifically focusing on methods for extreme-value analysis of univariate and multivariate data distributions. It introduces some of the earliest and most fundamental statistical methods for outlier detection, including probabilistic tail inequalities like the Markov inequality and Chebychev inequality, which can be used to determine the probability that an extreme value should be considered anomalous. It also discusses how extreme-value analysis methods can be extended from univariate to multivariate data and how mixture models provide a probabilistic approach to identifying both outliers and extreme values.
Logistic regression - one of the key regression tools in experimental researchAdrian Olszewski
Despite the wrong (yet widespread) claim, that "logistic regression is not a regression", it's one of the key regression tool in experimental research, like the clinical trials. It is used also for advanced testing hypotheses.
The logistic regression is part of the GLM (Generalized Linear Model) regression framework.
1. The document describes a project to predict customer churn for a telecom company using logistic regression, KNN, and Naive Bayes models.
2. Exploratory data analysis was conducted on usage, contract, payment and other customer data, finding some variable correlation.
3. Logistic regression performed best with 75% accuracy. KNN accuracy was also good with K=2.
4. The models identified contract renewal and monthly charges as critical factors for churn, suggesting the company focus on these areas.
This document provides an analysis and application of the Markov Switching Multifractal (MSM) volatility model. The author applies the MSM to daily log-returns of the S&P 500, S&P 100, VIX, and VXO indices. The MSM constructs a multifractal model with over 1,000 states but only 4 parameters. It outperforms a normal distribution GARCH model in-sample and out-of-sample, though not a Student's t-distribution GARCH. However, the MSM forecasts volatility significantly better than both GARCH models at horizons of 20-50 days.
This document describes the variable transformation and selection process used in an R tool for credit scoring. The process involves binning variables, transforming them to weights of evidence (WoE), clustering variables, and selecting representative variables for modeling based on information value and cluster relationships. The tool is aimed at addressing issues with mixed, malformed, missing, and correlated credit risk variables when developing credit risk scorecards.
This document discusses forecasting covariance matrices using the Dynamic Conditional Correlation (DCC) GARCH model. It begins with an overview of univariate GARCH models and the GARCH(1,1) specification. It then introduces the DCC model, which models the conditional covariance matrix indirectly through the conditional correlation matrix. The document evaluates how forecasts from the DCC model perform compared to a covariance matrix based only on historical data. It presents an empirical application comparing the two approaches using different datasets. The conclusion discusses how the DCC model tends to outperform the historical covariance matrix in the short-run but the reverse is true in the long-run.
Classification of mathematical modeling,
Classification based on Variation of Independent Variables,
Static Model,
Dynamic Model,
Rigid or Deterministic Models,
Stochastic or Probabilistic Models,
Comparison Between Rigid and Stochastic Models
- Multinomial logistic regression predicts categorical membership in a dependent variable based on multiple independent variables. It is an extension of binary logistic regression that allows for more than two categories.
- Careful data analysis including checking for outliers and multicollinearity is important. A minimum sample size of 10 cases per independent variable is recommended.
- Multinomial logistic regression does not assume normality, linearity or homoscedasticity like discriminant function analysis does, making it more flexible and commonly used. It does assume independence between dependent variable categories.
This paper is a methodological exercices presenting the results obtained from the estimation of the growth convergence equation using different methodologies.
A dynamic balanced panel data is estimated using: OLS, WithinGroup, HsiaoAnderson, First Difference, GMM with endogenous and GMM with predetermined instruments. An unbalanced panel is also realized for OLS, WG and FD.
Results are discused in light of Monte Carlo studies.
Decentralized data fusion approach is one in which features are extracted and processed individually and finally fused to obtain global estimates. The paper presents decentralized data fusion algorithm using factor analysis model. Factor analysis is a statistical method used to study the effect and interdependence of various factors within a system. The proposed algorithm fuses accelerometer and gyroscope data in an inertial measurement unit (IMU). Simulations are carried out on Matlab platform to illustrate the algorithm.
High performance Serverless Java on AWS- GoTo Amsterdam 2024Vadym Kazulkin
Java is for many years one of the most popular programming languages, but it used to have hard times in the Serverless community. Java is known for its high cold start times and high memory footprint, comparing to other programming languages like Node.js and Python. In this talk I'll look at the general best practices and techniques we can use to decrease memory consumption, cold start times for Java Serverless development on AWS including GraalVM (Native Image) and AWS own offering SnapStart based on Firecracker microVM snapshot and restore and CRaC (Coordinated Restore at Checkpoint) runtime hooks. I'll also provide a lot of benchmarking on Lambda functions trying out various deployment package sizes, Lambda memory settings, Java compilation options and HTTP (a)synchronous clients and measure their impact on cold and warm start times.
Conversational agents, or chatbots, are increasingly used to access all sorts of services using natural language. While open-domain chatbots - like ChatGPT - can converse on any topic, task-oriented chatbots - the focus of this paper - are designed for specific tasks, like booking a flight, obtaining customer support, or setting an appointment. Like any other software, task-oriented chatbots need to be properly tested, usually by defining and executing test scenarios (i.e., sequences of user-chatbot interactions). However, there is currently a lack of methods to quantify the completeness and strength of such test scenarios, which can lead to low-quality tests, and hence to buggy chatbots.
To fill this gap, we propose adapting mutation testing (MuT) for task-oriented chatbots. To this end, we introduce a set of mutation operators that emulate faults in chatbot designs, an architecture that enables MuT on chatbots built using heterogeneous technologies, and a practical realisation as an Eclipse plugin. Moreover, we evaluate the applicability, effectiveness and efficiency of our approach on open-source chatbots, with promising results.
Connector Corner: Seamlessly power UiPath Apps, GenAI with prebuilt connectorsDianaGray10
Join us to learn how UiPath Apps can directly and easily interact with prebuilt connectors via Integration Service--including Salesforce, ServiceNow, Open GenAI, and more.
The best part is you can achieve this without building a custom workflow! Say goodbye to the hassle of using separate automations to call APIs. By seamlessly integrating within App Studio, you can now easily streamline your workflow, while gaining direct access to our Connector Catalog of popular applications.
We’ll discuss and demo the benefits of UiPath Apps and connectors including:
Creating a compelling user experience for any software, without the limitations of APIs.
Accelerating the app creation process, saving time and effort
Enjoying high-performance CRUD (create, read, update, delete) operations, for
seamless data management.
Speakers:
Russell Alfeche, Technology Leader, RPA at qBotic and UiPath MVP
Charlie Greenberg, host
LF Energy Webinar: Carbon Data Specifications: Mechanisms to Improve Data Acc...DanBrown980551
This LF Energy webinar took place June 20, 2024. It featured:
-Alex Thornton, LF Energy
-Hallie Cramer, Google
-Daniel Roesler, UtilityAPI
-Henry Richardson, WattTime
In response to the urgency and scale required to effectively address climate change, open source solutions offer significant potential for driving innovation and progress. Currently, there is a growing demand for standardization and interoperability in energy data and modeling. Open source standards and specifications within the energy sector can also alleviate challenges associated with data fragmentation, transparency, and accessibility. At the same time, it is crucial to consider privacy and security concerns throughout the development of open source platforms.
This webinar will delve into the motivations behind establishing LF Energy’s Carbon Data Specification Consortium. It will provide an overview of the draft specifications and the ongoing progress made by the respective working groups.
Three primary specifications will be discussed:
-Discovery and client registration, emphasizing transparent processes and secure and private access
-Customer data, centering around customer tariffs, bills, energy usage, and full consumption disclosure
-Power systems data, focusing on grid data, inclusive of transmission and distribution networks, generation, intergrid power flows, and market settlement data
Must Know Postgres Extension for DBA and Developer during MigrationMydbops
Mydbops Opensource Database Meetup 16
Topic: Must-Know PostgreSQL Extensions for Developers and DBAs During Migration
Speaker: Deepak Mahto, Founder of DataCloudGaze Consulting
Date & Time: 8th June | 10 AM - 1 PM IST
Venue: Bangalore International Centre, Bangalore
Abstract: Discover how PostgreSQL extensions can be your secret weapon! This talk explores how key extensions enhance database capabilities and streamline the migration process for users moving from other relational databases like Oracle.
Key Takeaways:
* Learn about crucial extensions like oracle_fdw, pgtt, and pg_audit that ease migration complexities.
* Gain valuable strategies for implementing these extensions in PostgreSQL to achieve license freedom.
* Discover how these key extensions can empower both developers and DBAs during the migration process.
* Don't miss this chance to gain practical knowledge from an industry expert and stay updated on the latest open-source database trends.
Mydbops Managed Services specializes in taking the pain out of database management while optimizing performance. Since 2015, we have been providing top-notch support and assistance for the top three open-source databases: MySQL, MongoDB, and PostgreSQL.
Our team offers a wide range of services, including assistance, support, consulting, 24/7 operations, and expertise in all relevant technologies. We help organizations improve their database's performance, scalability, efficiency, and availability.
Contact us: info@mydbops.com
Visit: https://www.mydbops.com/
Follow us on LinkedIn: https://in.linkedin.com/company/mydbops
For more details and updates, please follow up the below links.
Meetup Page : https://www.meetup.com/mydbops-databa...
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5th LF Energy Power Grid Model Meet-up SlidesDanBrown980551
5th Power Grid Model Meet-up
It is with great pleasure that we extend to you an invitation to the 5th Power Grid Model Meet-up, scheduled for 6th June 2024. This event will adopt a hybrid format, allowing participants to join us either through an online Mircosoft Teams session or in person at TU/e located at Den Dolech 2, Eindhoven, Netherlands. The meet-up will be hosted by Eindhoven University of Technology (TU/e), a research university specializing in engineering science & technology.
Power Grid Model
The global energy transition is placing new and unprecedented demands on Distribution System Operators (DSOs). Alongside upgrades to grid capacity, processes such as digitization, capacity optimization, and congestion management are becoming vital for delivering reliable services.
Power Grid Model is an open source project from Linux Foundation Energy and provides a calculation engine that is increasingly essential for DSOs. It offers a standards-based foundation enabling real-time power systems analysis, simulations of electrical power grids, and sophisticated what-if analysis. In addition, it enables in-depth studies and analysis of the electrical power grid’s behavior and performance. This comprehensive model incorporates essential factors such as power generation capacity, electrical losses, voltage levels, power flows, and system stability.
Power Grid Model is currently being applied in a wide variety of use cases, including grid planning, expansion, reliability, and congestion studies. It can also help in analyzing the impact of renewable energy integration, assessing the effects of disturbances or faults, and developing strategies for grid control and optimization.
What to expect
For the upcoming meetup we are organizing, we have an exciting lineup of activities planned:
-Insightful presentations covering two practical applications of the Power Grid Model.
-An update on the latest advancements in Power Grid -Model technology during the first and second quarters of 2024.
-An interactive brainstorming session to discuss and propose new feature requests.
-An opportunity to connect with fellow Power Grid Model enthusiasts and users.
In the realm of cybersecurity, offensive security practices act as a critical shield. By simulating real-world attacks in a controlled environment, these techniques expose vulnerabilities before malicious actors can exploit them. This proactive approach allows manufacturers to identify and fix weaknesses, significantly enhancing system security.
This presentation delves into the development of a system designed to mimic Galileo's Open Service signal using software-defined radio (SDR) technology. We'll begin with a foundational overview of both Global Navigation Satellite Systems (GNSS) and the intricacies of digital signal processing.
The presentation culminates in a live demonstration. We'll showcase the manipulation of Galileo's Open Service pilot signal, simulating an attack on various software and hardware systems. This practical demonstration serves to highlight the potential consequences of unaddressed vulnerabilities, emphasizing the importance of offensive security practices in safeguarding critical infrastructure.
Skybuffer SAM4U tool for SAP license adoptionTatiana Kojar
Manage and optimize your license adoption and consumption with SAM4U, an SAP free customer software asset management tool.
SAM4U, an SAP complimentary software asset management tool for customers, delivers a detailed and well-structured overview of license inventory and usage with a user-friendly interface. We offer a hosted, cost-effective, and performance-optimized SAM4U setup in the Skybuffer Cloud environment. You retain ownership of the system and data, while we manage the ABAP 7.58 infrastructure, ensuring fixed Total Cost of Ownership (TCO) and exceptional services through the SAP Fiori interface.
For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/temporal-event-neural-networks-a-more-efficient-alternative-to-the-transformer-a-presentation-from-brainchip/
Chris Jones, Director of Product Management at BrainChip , presents the “Temporal Event Neural Networks: A More Efficient Alternative to the Transformer” tutorial at the May 2024 Embedded Vision Summit.
The expansion of AI services necessitates enhanced computational capabilities on edge devices. Temporal Event Neural Networks (TENNs), developed by BrainChip, represent a novel and highly efficient state-space network. TENNs demonstrate exceptional proficiency in handling multi-dimensional streaming data, facilitating advancements in object detection, action recognition, speech enhancement and language model/sequence generation. Through the utilization of polynomial-based continuous convolutions, TENNs streamline models, expedite training processes and significantly diminish memory requirements, achieving notable reductions of up to 50x in parameters and 5,000x in energy consumption compared to prevailing methodologies like transformers.
Integration with BrainChip’s Akida neuromorphic hardware IP further enhances TENNs’ capabilities, enabling the realization of highly capable, portable and passively cooled edge devices. This presentation delves into the technical innovations underlying TENNs, presents real-world benchmarks, and elucidates how this cutting-edge approach is positioned to revolutionize edge AI across diverse applications.
What is an RPA CoE? Session 1 – CoE VisionDianaGray10
In the first session, we will review the organization's vision and how this has an impact on the COE Structure.
Topics covered:
• The role of a steering committee
• How do the organization’s priorities determine CoE Structure?
Speaker:
Chris Bolin, Senior Intelligent Automation Architect Anika Systems
This talk will cover ScyllaDB Architecture from the cluster-level view and zoom in on data distribution and internal node architecture. In the process, we will learn the secret sauce used to get ScyllaDB's high availability and superior performance. We will also touch on the upcoming changes to ScyllaDB architecture, moving to strongly consistent metadata and tablets.
Northern Engraving | Modern Metal Trim, Nameplates and Appliance PanelsNorthern Engraving
What began over 115 years ago as a supplier of precision gauges to the automotive industry has evolved into being an industry leader in the manufacture of product branding, automotive cockpit trim and decorative appliance trim. Value-added services include in-house Design, Engineering, Program Management, Test Lab and Tool Shops.
"Frontline Battles with DDoS: Best practices and Lessons Learned", Igor IvaniukFwdays
At this talk we will discuss DDoS protection tools and best practices, discuss network architectures and what AWS has to offer. Also, we will look into one of the largest DDoS attacks on Ukrainian infrastructure that happened in February 2022. We'll see, what techniques helped to keep the web resources available for Ukrainians and how AWS improved DDoS protection for all customers based on Ukraine experience
Session 1 - Intro to Robotic Process Automation.pdfUiPathCommunity
👉 Check out our full 'Africa Series - Automation Student Developers (EN)' page to register for the full program:
https://bit.ly/Automation_Student_Kickstart
In this session, we shall introduce you to the world of automation, the UiPath Platform, and guide you on how to install and setup UiPath Studio on your Windows PC.
📕 Detailed agenda:
What is RPA? Benefits of RPA?
RPA Applications
The UiPath End-to-End Automation Platform
UiPath Studio CE Installation and Setup
💻 Extra training through UiPath Academy:
Introduction to Automation
UiPath Business Automation Platform
Explore automation development with UiPath Studio
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Taking AI to the Next Level in Manufacturing.pdfssuserfac0301
Read Taking AI to the Next Level in Manufacturing to gain insights on AI adoption in the manufacturing industry, such as:
1. How quickly AI is being implemented in manufacturing.
2. Which barriers stand in the way of AI adoption.
3. How data quality and governance form the backbone of AI.
4. Organizational processes and structures that may inhibit effective AI adoption.
6. Ideas and approaches to help build your organization's AI strategy.
inQuba Webinar Mastering Customer Journey Management with Dr Graham HillLizaNolte
HERE IS YOUR WEBINAR CONTENT! 'Mastering Customer Journey Management with Dr. Graham Hill'. We hope you find the webinar recording both insightful and enjoyable.
In this webinar, we explored essential aspects of Customer Journey Management and personalization. Here’s a summary of the key insights and topics discussed:
Key Takeaways:
Understanding the Customer Journey: Dr. Hill emphasized the importance of mapping and understanding the complete customer journey to identify touchpoints and opportunities for improvement.
Personalization Strategies: We discussed how to leverage data and insights to create personalized experiences that resonate with customers.
Technology Integration: Insights were shared on how inQuba’s advanced technology can streamline customer interactions and drive operational efficiency.
How information systems are built or acquired puts information, which is what they should be about, in a secondary place. Our language adapted accordingly, and we no longer talk about information systems but applications. Applications evolved in a way to break data into diverse fragments, tightly coupled with applications and expensive to integrate. The result is technical debt, which is re-paid by taking even bigger "loans", resulting in an ever-increasing technical debt. Software engineering and procurement practices work in sync with market forces to maintain this trend. This talk demonstrates how natural this situation is. The question is: can something be done to reverse the trend?
1. ATHENS UNIVERSITY OF ECONOMICS AND BUSINESS
DEPARTMENT OF STATISTICS
Efficient
Bayesian Marginal Likelihood
estimation in
Generalised Linear Latent Variable Models
thesis submitted by
Silia Vitoratou
advisors
Ioannis Ntzoufras
Irini Moustaki
Athens, 2013
3. Chapter 1
Key ideas and origins of the latent variable models (LVM).
“...co-relation must be the consequence of the variations
of the two organs being partly due to common causes ...“
Francis Galton, 1888.
• Suppose we want to infer for concepts that cannot be measured directly (such
as emotions, attitudes, perceptions, proficiency etc).
• We assume that they can be measured indirectly through other observed
items.
• The key idea is that all dependencies among p-manifest variables (observed
items) are attributed to k-latent (unobserved) ones.
• By principle, k << p. Hence, at the same time, the LVM methodology is a
multivariate analysis technique which aims to reduce the dimensionality, with
as little loss of information as possible.
3
4. Chapter 1
A unified approach: Generalised linear latent variable
models (GLLVM).
Generalized linear latent variable model (GLLVM; Bartholomew &Knott, 1999; Skrondal and
Rabe-Hesketh, 2004) . The models assumes that the response variables are linear combinations
of the latent ones and it consists of three components:
(a) the multivariate random component: where each observed item Yj, (j = 1, ..., p)
has a distribution from the exponential family (Bernoulli, Multinomial, Normal,
Gamma),
(b) the systematic component: where the latent variables Zℓ, ℓ = 1, ..., k, produce the
linear predictor ηj for each Yj
(c) the link function : which connects the previous two components
4
5. Chapter 1
A unified approach: Generalised linear latent variable
models (GLLVM).
Special case: Generalized linear latent trait model- with binary items (Moustaki
&Knott, 2000) .
The conditionals
are in this case Bernoulli(
), where
is
the conditional probability of a positive response to the observed item. The
logistic model is used for the response probabilities:
• The item parameters
are often referred to as the difficulty and
the discrimination parameters (respectively) of the item j.
All examples considered in this thesis refer to multivariate IRT (2-PL) models.
Current findings apply directly or can be expanded to any type of GLLVM.
5
6. Chapter 1
A unified approach: Generalised linear latent variable
models (GLLVM).
As only the p-items can be observed, any inference must be based on their joint
distribution.
All data dependencies are attributed to the existence of the latent variables.
Hence, the observed variables are assumed independent given the latent (local
independence assumption) :
where
is the prior distribution for the latent variables. A fully Bayesian
approach requires that the item parameter vector
is also
stochastic, associated with a prior probability.
6
7. Chapter 2
The fully Bayesian analogue: GLLTM with binary items
A) Priors
All model parameters are assumed a-priori independent
where
Prior from
Ntzoufras et al. (2000)
Fouskakis et al. (2009)
leading to
For unique solution we use the
Cholesky decomposition on B:
7
8. Chapter 2
The fully Bayesian analogue: GLLTM with binary items
B) Sampling from the posterior
• A Metropolis-within-Gibbs algorithm initially presented for IRT models by Patz and
Junker (1996) was used here for the multivariate case (k>1).
• Each item is updated in one block. So are the latent variables for each person.
C) Model evaluation
• In this thesis, the Bayes Factor (BF; Jeffreys, 1961; Kass and Raftery, 1995) was used for
model comparison.
• The BF is defined as the ratio of the posterior odds of two competing models (say m1
and m2) multiplied by their corresponding prior odds. Provided that the models have
equal prior probabilities, is given by:
that is, the ratio of the two models’ marginal or integrated likelihoods (hereafter
Bayesian marginal likelihood; BML).
8
9. Chapter 2
Estimating the Bayesian marginal likelihood
The BML (also known as the prior predictive distribution) is defined as the
expected model likelihood over the model parameters’ prior:
that quite often is a high dimensional integral, not available in closed form.
Monte Carlo integration is often used to estimate it, as for instance the
arithmetic mean:
This simple estimator does not really work adequately and a plethora of
Markov chains Monte Carlo (MCMC) techniques are employed instead in the
literature.
9
10. Chapter 2
Estimating the Bayesian marginal likelihood
The point based estimators (PBE) employ the candidates’ identity (Besag, 1989),
in a point of high density:
• Laplace-Metropolis (LM; Lewis & Raftery, 1997)
• Gaussian copula (GC; Nott et al, 2008)
• Chib & Jeliazkov (CJ; Chib & Jeliazkov, 2001)
The bridge sampling estimators (BSE), employ a bridge function
, based
on the form of which, several BML identities can be derived (even pre–
existing):
• Harmonic mean (HM; Newton & Raftery, 1994)
• Reciprocal mean (RM; Gelfand & Dey, 1994)
• Bridge harmonic (BH; Meng & Wong, 1996)
• Bridge geometric (BG; Meng & Wong, 1996)
The path sampling estimators (PSE), employ a continuous and differential
path
, to link two un-normalised densities and compute the ratio of the
corresponding constants:
• Power posteriors (PPT; Friel & Pettitt, 2008; Lartillot &Philippe, 2006)
• Steppingstone (PPS ; Xie at al, 2011)
• Generalised steppingstone (IPS; Fan et al, 2011)
10
11. Chapter 3
The behavior of joint and marginal Monte Carlo estimators in multi-parameter latent variable models
Monte Carlo integration: the case of GLLVM
From the early readings the methods applied for the parameter estimation of
model settings with latent variables relied on the
joint likelihood
Lord and Novick, 1968;
Lord,1980
or the
marginal likelihood
Bock and Aitkin, 1981;
Moustaki and Knott, 2000
Under the conditional independence assumptions of the GLLVMs, there are two
equivalent formulations of the BML, which lead to different MC estimators, namely the
joint BML
and the
marginal BML
11
12. Chapter 3
The behavior of joint and marginal Monte Carlo estimators in multi-parameter latent variable models
Monte Carlo integration: the case of GLLVM
A motivating example
A simulated data set with p = 6 items, N = 600 cases and k = 2 factors was considered.
Three popular BSE were computed under both approaches (R= 50,000 posterior
observations , after burn in period of 10,000 and thinning interval of 10).
• BH: Largest error difference
but rather close estimation...
• BG: Largest difference in the
estimation without large error
difference...
Differences are due to Monte
Carlo integration, under
independence assumptions
12
13. Chapter 3
The behavior of joint and marginal Monte Carlo estimators in multi-parameter latent variable models
Monte Carlo integration: the case of GLLVM
The joint version of BH comes with much
higher MCE than the RM...
...but is the joint version of RM that fails to
converge to the true value.
?
13
14. Chapter 3
The behavior of joint and marginal Monte Carlo estimators in multi-parameter latent variable models
Monte Carlo integration under independence
•
Consider any integral of the form:
•
The corresponding MC estimator is:
assuming a random sample of points drawn from h
•
The corresponding Monte Carlo Error (MCE) is:
•
Assume independence, that is,
hence
14
15. Chapter 3
The behavior of joint and marginal Monte Carlo estimators in multi-parameter latent variable models
Monte Carlo integration under independence
The two estimators are associated with different MCEs. Based on the early results of
Goodman (1962), for the variance of N independent variables, the variances of the
estimators are:
for each term
In finite settings, the difference can be outstanding
15
16. Chapter 3
The behavior of joint and marginal Monte Carlo estimators in multi-parameter latent variable models
Monte Carlo integration under independence
In particular, the difference in the variances is given by
Naturally, it depends on R. Note however that also it depends on
• dimensionality (N), since more positive terms are added, and
• on the means and variances of the N variables involved
At the same time, the difference in the means is given by
• Total covariation index (multivariate extension of the covariance).
• Under independence the index should be zero (the reverse statement does not hold)
• At the sample, the covariances, no matter how small, are non-zero leading to non zero TCI.
•Depends also on the number of the variables (N), their means, and their variation through the
covariances
16
17. Chapter 3
The behavior of joint and marginal Monte Carlo estimators in multi-parameter latent variable models
Monte Carlo integration: the case of GLLVM
A motivating example-Revisited
Different
variables are
being
averaged,
leading to
different
variance
components
Total covariance cancels out for the BH.
17
18. Chapter 3
The behavior of joint and marginal Monte Carlo estimators in multi-parameter latent variable models
Monte Carlo integration & independence
Refer to Chapter 3 of the current thesis for:
•
more results on the error difference,
•
properties of the TCI,
•
extension to conditional independence,
•
and more illustrative examples.
18
19. Chapter 4
Bayesian marginal likelihood estimation using the Metropolis kernel in multi-parameter latent variable models
Basic idea
Based on the work of Chib & Jeliazkov(2001), it is shown in Chapter 3 that the
Metropolis kernel can be used to marginalise out any subset of the parameter vector,
that otherwise would not be feasible.
• Consider the kernel of the Metropolis – Hastings algorithm, which denotes the
transition probability of sampling
, given that
has been already generated:
Transition
probability
Acceptance
probability
Proposal
density
• Then, the latent vector can be marginalised out directly from the Metropolis kernel as
follows:
19
20. Chapter 4
Bayesian marginal likelihood estimation using the Metropolis kernel in multi-parameter latent variable models
Chib & Jeliazkov estimator
Let us suppose that the parameter space is divided into p blocks of parameters. Then, using the Law
of total probability, the posterior at a specific point can be decomposed to
• If analytically available use candidates’ (Besag, 1989) formula to compute the BML directly.
• If the full conditionals are known, Chib (1995) uses the output from the Gibbs sampler to estimate them.
• Otherwise Chib and Jeliazkov (2001) show that each posterior ordinate can be computed by
Requires p
sequential
MCMC
runs.
20
21. Chapter 4
Bayesian marginal likelihood estimation using the Metropolis kernel in multi-parameter latent variable models
Chib & Jeliazkov estimator for models with latent vectors
The number of latent variables can be hundreds if not thousands. Hence the method is time
consuming. Chib & Jeliazkov suggest to use the last ordinate to marginalise out the latent vector,
provided that
is analytically tractable (often it is not).
In Chapter 4 of the thesis, it is shown that the latent vector can be marginalised out directly from
the MH kernel, as follows:
Hence the
dimension of the
latent vector is
not an issue.
This observation however leads to another result. Assuming local independence, prior
independence and a Metropolis - within – Gibbs algorithm, as in the case of the GLLVM, the Chib
& Jeliazkov identity is drastically simplified as follows:
Hence the number
of blocks , also, is
not an issue.
• The latent vector is marginalised out as previously.
• Moreover, even there are p-blocks for the model parameters, only the full MCMC is required.
• Can be used under data augmentations schemes that produce independence
21
22. Chapter 4
Bayesian marginal likelihood estimation using the Metropolis kernel in multi-parameter latent variable models
Independence Chib & Jeliazkov estimator
Three simulated data sets – under different scenarios. Compare CJI with ML estimators.
Rtotal
1st batch
30 batches
1000
2000
3000
iterations
per batch
22
23. Chapter 6
Implementation in simulated and real life datasets
Some results
•p =6 items,
•N=600 individuals,
•k=1 factor
kmodel = ktrue
23
24. Chapter 6
Implementation in simulated and real life datasets
Some results
•p =6 items,
•N=600 individuals,
•k=2 factors
kmodel = ktrue
24
25. Chapter 6
Implementation in simulated and real life datasets
Some results
•p =8 items,
•N=700 individuals,
•k=3 factor
kmodel = ktrue
25
26. Chapter 6
Implementation in simulated and real life datasets
Some results
•p =6 items,
•N=600 individuals,
•k=1 factor
kmodel <ktrue
26
27. Chapter 6
Implementation in simulated and real life datasets
Some results
•p =6 items,
•N=600 individuals,
•k=2 factors
kmodel >ktrue
27
28. Chapter 6
Implementation in simulated and real life datasets
Concluding comments
Refer to Chapter 4 of the current thesis for more details on the implementation of the CJI
(or see Vitoratou et al, 2013) :
More comparisons are presented in Chapter 6 of the thesis, in simulated and real data
sets. Some comments:
• The harmonic mean failed in all cases.
• The BSE were successful in all examples.
o The BG estimator was consistently associated with the smallest error.
o The RM was also well behaved in all cases.
o The BH was associated with more error that the former two BSE.
• The PBE are well behaved:
o LM is very quick and efficient – but might fail if the posterior is not symmetrical.
o Similarly for the GC.
o CJI is well behaved but time consuming. Since it is distributional free, can be used
as a benchmark method to get an idea of the BML.
28
29. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamics and Bayes
Ideas initially implemented in thermodynamics are currently explored in Bayesian
model evaluation.
Assume two unnormalised densities (q1 and q0) and we are interested in the
ratio of their normalising constants (λ).
For that purpose we use a continuous and differential function of the form
geometric path which
links the endpoint densities
temperature parameter
Boltzmann-Gibbs distribution
Partition function
Then the ratio λ can be computed via the thermodynamic integration identity (TI):
Bayes free energy
29
30. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamics and BML: Power Posteriors
The first application of the TI to the problem of estimating the BML is the power
posteriors (PP) method (Friel and Pettitt, 2008; Lartillot and Philippe, 2006). Let
then
prior-posterior path
power posterior
leading via the thermodynamic integration to the Bayesian marginal likelihood
For ts close to 0 we
sample from densities
close to the prior,
where the variability is
typically high.
30
31. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamics and BML: Importance Posteriors
Lefebvre et al. (2010) considered other options than the prior for the zero
endpoint, keeping the unnormalised posterior at the unit endpoint. Any proper
density g() will do:
An appealing option is to use an importance (envelope) function, that is a
density as close as possible to the posterior).
importance-posterior path
importance posterior
For ts close to 0 we
sample from densities
close to the importance
function, solving the
problem
of
high
variability.
31
32. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
An alternative approach: stepping-stone identities
Xie et al (2011) using the prior and the posterior as endpoint densities, considered a different approach
to compute the BMI, also related to thermodynamics (Neal, 1993). First, the interval [0,1] is partitioned
into n points and the free energy can be computed as:
Stepping
stone
• Under the power posteriors path, Xie et al (2011) showed that the BML occurs as:
• Under the importance posteriors path, Fan et al (2011) showed that the BML occurs as:
However, the stepping–stone identity (SI) is even more general and can be used under
different paths, as an alternative to the TI:
32
33. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Path sampling identities for the BML- revisited
Hence, there are two general identities to compute a ratio of normalising
constants, within the path sampling framework, namely
Different paths lead to different expressions for the BML:
Identity for the BML
path
TI
SI
Prior
posterior
Power posteriors (PPT)
Stepping-stone (PPS)
Importance
posterior
Importance posteriors (IPT)
Generalised stepping stone (IPS)
Friel and Pettitt, 2008
Lartillot and Philippe, 2006
inspired by Lefebvre et al. (2010)
Xie et al (2011)
Fan et al (2011)
Other paths can be used, under both approaches, to derive identities
for the BML or any other ratio of normalising constants.
Hereafter, the identities with be named by the path employed, with a
subscript denoting the method implemented, e.g. IPS
33
34. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamics & direct BF identities: Model switching
Lartillot and Philippe (2006) considered as endpoint densities the unormalised
posteriors of two competing models:
leading to the model switching path
leading via the thermodynamic integration to the Bayes Factor
bidirectional
melting-annealing
sampling scheme.
While it is easy to derive the SI counterpart expression:
34
35. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamics & direct BF identities: Quadrivials
Based on the idea of Lartillot and Philippe (2006) we may proceed with the compound paths.
which consist of
• a hyper, geometric path
which links two competing models, and
• a nested, geometric path
for each endpoint function Qi , i=0,1.
The two intersecting paths form a quadrivial
Which can be used either with the TI or the SI approach. If the ratio of interest is the BF, the two
BMLs should be derived at the endpoints of [0,1]. The PP and the IP paths are natural choices for
the nested part of the identity. For the latter
35
36. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Sources of error in path sampling estimators
a) The integral over [0,1] in the TI is typically approximated via numerical
approaches, such as the trapezoidal or Simpson’s rule (Neal, 1993; Gelman and
Meng, 1998), which require an n-point discretisation of [0,1]:
Note that the temperature schedule is also required for the SI method (it defines
the stepping stone ratios) . The discretisation introduces error to the TI and SI
estimators, that is referred to as the discretisation error.
It can be reduced by a) increasing the number of points n and/or b) by assigning
more points closer to the endpoint that is associated higher variability.
b) At each point
the corresponding
, a separate MCMC run is performed with target distribution
. Hence, Monte Carlo error occurs also at each run.
c) As a third source of error can be considered also the path-related error.
We may gain insight into a) and c) by considering the measures of
entropy related to the TI.
36
37. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Performance: Pine data-a simple regression example
Measurements taken on 42 specimens. A linear regression model was fitted for the
specimen’s maximum compressive strength (y), using their density (x) as independent
variable:
The objective in this example is to illustrate how each method and path combination
responds to prior uncertainty. To do so, we use three different prior schemes, namely:
The ratios of the corresponding BMLs under the three priors were estimated over n1 = 50
and n2 = 100 evenly spaced temperatures. At each temperature, a Gibbs algorithm was
implemented and 30,000 posterior observations were generated; after discarding 5,000 as a
burn-in period.
37
38. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Performance: Pine data-a simple regression example
Implementing a uniform temperature schedule:
Reflects
difference
in the
path-related
error
Reflects
difference
in the
discretisation
error
All quadrivals
come with
smaller batch
mean error
Note: PP works just fine under a geometric temperature schedule that samples
more points from the prior.
38
39. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamic integration & distribution divergencies
Based on the prior-posterior path, Friel and Pettitt (2008) and Lefebvre et al. (2010)
showed that the PP method is connected with the Kullback – Leibler diveregence
(KL; Kullback & Leibler, 1951).
Relative entropy
Differential entropy
Cross entropy
Here we present their findings on a general form, that is, for any geometric path
according to the TI
it holds that
symmetrised KL
39
40. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamic integration & distribution divergencies
Graphical representation of the TI
What about
the
intermediate
points?
40
41. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamic integration & distribution divergencies
TI minus free energy at each point
Instead of integrating
the mean energy over
the entire interval [0,1],
there is an optimal
temperature, where the
mean energy equals the
free energy.
41
42. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamic integration & distribution divergencies
Graphical representation of the NTI
functional KL
difference in the
KL-distance of
the sampling
distribution pt
from p1 and p0
The ratio of
interest occurs at
the point
where the
sampling
distribution is
equidistant from
the endpoint
densities
42
43. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamic integration & distribution divergencies
The normalised thermodynamic integral
Hence:
•According to the PPT method, the BML occurs at the point where the sampling
distribution is equidistant from the prior and the posterior.
•According to the QMST method, the BF occurs at the point where the sampling
distribution is equidistant from the two posteriors.
The sampling distribution pt is the Boltzmann-Gibbs distribution pertaining to the Hamiltonian
(energy function)
. Therefore
•according to the NTI, when geometric paths are employed, the free energy
occurs at the point where the Boltzmann-Gibbs distribution is equidistant from the
distributions at the endpoint states.
43
44. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamic integration & distribution divergencies
Graphical representation of the NTI
What are
the areas
stand for?
44
45. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamic integration & distribution divergencies
The normalised thermodynamic integral and probability distribution divergencies
A key observation here is that the sampling distribution embodies the Chernoff coefficient
(Chernoff, 1952) :
Based on that, the NTI can be written as:
meaning that
and therefore, the areas correspond to the Chernoff t-divergence. At t=t*, we obtain
the so-called Chernoff information:
45
46. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamic integration & distribution divergencies
Using the output from path sampling, the Chernoff divergence can be
computed easily (see Chapter 5 of the thesis for a step-by step algorithm).
Along with the Chernoff estimation, a number of other f-divergencies can
be directly estimated, namely
• the Bhattacharyya distance (Bhattacharyya, 1943) at t = 0.5,
• the Hellinger distance (Bhattacharyya, 1943; Hellinger, 1909),
• the Rényi t-divergence (Rényi, 1961) and
• the Tsallis t-relative entropy (Tsallis, 2001) .
These measures of entropy are commonly used in
• information theory, pattern recognition, cryptography, machine learning,
• hypothesis testing
• and recently, in non-equilibrium thermodynamics.
46
47. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Thermodynamic integration & distribution divergencies
Measures of entropy and the NTI
47
48. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Path selection, temperature schedule and error.
These results provide insight also on the error of the path sampling estimators. To begin with
Lefebre et al (2010) have showed that the total variance is associated with the J−divergence of
the endpoint densities and therefore with the choice of the path. Graphically
• the J-distance
coincides with the
slope of the secant
defined at the
endpoint densities.
The shape of the
curve is a
graphical
representation of
the total
variance.
• the slope of the tangent at
a particular point ti,
coincides with the local
variance
Higher local
variances, at the
points where the
curve is steeper.
• the graphical
representation of two
competing paths provides
information about the
estimators’ variances.
Paths with
smaller cliffs are
easier to take!
48
49. Chapter 5
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Path selection, temperature schedule and error.
Numerical approximation of the TI:
Assign more tis at points where the curve is steeper (higher local variances)
Different level
of accuracy
towards the
two endpoints
The discretization
error depends
primarily on the
path
49
50. Future work
Currently developing a library in R for BML estimation in GLLTM with Danny Arends.
Expand results (and R library) to account for other type of data.
Further study on the TCI (Chapter 3).
Use the ideas in Chapter 4 to construct a better Metropolis algorithm for GLLVMs.
Proceed further on the ideas presented in Chapter 5, with regard to the quadrivials, the
temperature schedule and the optimal t*. Explore applications to information criteria.
50
51. Bibliography
Bartholomew, D. and Knott, M. (1999). Latent variable models and factor analysis. Kendall’s Library of Statistics, 7. Wiley.
Bhattacharyya, A. (1943). On a measure of divergence between two statistical populations defined by their probability distributions. Bulletin of
the Calcutta Mathematical Society, 35:99–109.
Besag, J. (1989). A candidate’s formula: A curious result in Bayesian prediction. Biometrika, 76:183.
Bock, R. and Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika,
46:443–459.
Chernoff, H. (1952). A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. The Annals of Mathematical
Statistics, 23(4).
Chib, S. (1995). Marginal likelihood from the Gibbs output. Journal of the American Statistical Association, 90:1313–1321.
Chib, S. and Jeliazkov, I. (2001). Marginal likelihood from the Metropolis-Hastings output. Journal of the American Statistical Association,
96:270–281.
Fan, Y., Wu, R., Chen, M., Kuo, L., and Lewis, P. (2011). Choosing among partition models in Bayesian phylogenetics. Molecular Biology and
Evolution, 28(2):523–532.
Fouskakis, D., Ntzoufras, I., and Draper, D. (2009). Bayesian variable selection using cost-adjusted BIC, with application to cost-effective
measurement of quality of healthcare. Annals of Applied Statistics, 3:663–690.
Friel, N. and Pettitt, N. (2008). Marginal likelihood estimation via power posteriors. Journal of the Royal Statistical Society Series B (Statistical
Methodology), 70(3):589–607.
Gelfand, A. E. and Dey, D. K. (1994). Bayesian Model Choice: Asymptotics and exact calculations. Journal of the Royal Statistical Society. Series
B (Methodological), 56(3):501–514.
Gelman, A. and Meng, X. (1998). Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Statistical
Science, 13(2):163–185.
Goodman, L. A. (1962). The variance of the product of K random variables. Journal of the American Statistical Association, 57:54–60.
Hellinger, E. (1909). Neue Begr¨undung der Theorie quadratischer Formen von unendlichvielen Veranderlichen. Journal fddotur die reine und
angewandte Mathematik, 136:210–271.
Jeffreys, H. (1946). An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London. Series A,
Mathematical and Physical Sciences, 186(1007):453–461.
Kass, R. and Raftery, A. (1995). Bayes factors. Journal of the American Statistical Association, 90:773–795.
Kullback, S. and Leibler, R. A. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22:49–86.
Lewis, S. and Raftery, A. (1997). Estimating Bayes factors via posterior simulation with the Laplace Metropolis estimator. Journal of the
American Statistical Association, 92:648–655.
Lartillot, N. and Philippe, H. (2006). Computing Bayes factors using Thermodynamic Integration. Systematic Biology, 55:195–207.
Lefebvre, G., Steele, R., and Vandal, A. C. (2010). A path sampling identity for computing the Kullback-Leibler and J divergences.
Computational Statistics and Data Analysis, 54(7):1719–1731.
Lord, F. M. (1980). Applications of Item Response Theory to practical testing problems.Erlbaum Associates, Hillsdale, NJ.
Lord, F. M. and Novick, M. R. (1968). Statistical theories of mental test scores. Addison-Wesley, Oxford, UK
51
52. Meng, X.-L. and Wong, W.-H. (1996). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statistica
Sinica, 6:831–860.
Moustaki, I. and Knott, M. (2000). Generalized Latent Trait Models. Psychometrika, 65:391–411.
Neal, R. M. (1993). Probabilistic inference using Markov chain Monte Carlo methods.Technical Report CRG-TR-93-1, University of Toronto.
Newton, M. and Raftery, A. (1994). Approximate Bayesian inference with the weighted likelihood bootstrap. Journal of the Royal Statistical Society, 56:3–48.
Nott, D., Kohn, R., and Fielding, M. (2008). Approximating the marginal likelihood using copula. arXiv:0810.5474v1. Available at
http://arxiv.org/abs/0810.5474v1
Ntzoufras, I., Dellaportas, P., and Forster, J. (2000). Bayesian variable and link determination for Generalised Linear Models. Journal of Statistical Planning
and Inference,111(1-2):165–180.
Patz, R. J. and Junker, B. W. (1999b). A straightforward approach to Markov chain Monte Carlo methods for item response models. Journal of Educational
and Behavioral Statistics, 24(2):146–178.
Rabe-Hesketh, S., Skrondal, A., and Pickles, A. (2005). Maximum likelihood estimation of limited and discrete dependent variable models
with nested random effects. Journal of Econometrics, 128:301–323.
Raftery, A. and Banleld, J. (1991). Stopping the Gibbs sampler, the use of morphology, and other issues in spatial statistics. Annals of the Institute of
Statistical Mathematics, 43(430):32–43.
Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests. Paedagogiske Institut, Copenhagen.
Renyi, A. (1961). On measures of entropy and information. In Proceedings of the 4 th Berkeley Symposium on Mathematics, Statistics and Probability, pages
547–561.
Tsallis et al., Nonextensive Statistical Mechanics and Its Applications, edited by S.Abe and Y. Okamoto (Springer-Verlag, Heidelberg, 2001); see also the
comprehensive list of references at http://tsallis.cat.cbpf.br/biblio.htm.
Vitoratou, S., Ntzoufras, I., and Moustaki, I. (2013). Marginal likelihood estimation from the Metropolis output: tips and tricks for efficient implementation in
generalized linear latent variable models. To appear in: Journal of Statistical Computation and Simulation.
Xie, W., Lewis, P., Fan, Y., Kuo, L., and Chen, M. (2011). Improving marginal likelihood estimation for Bayesian phylogenetic model selection. Systematic
Biology, 60(2):150–160.
This thesis is dedicated to
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