Statistical Analysis of Imaging Trials: Multivariate Methods and Prediction, Probing Cancer with MR II: From Animal Models to Clinical Assessment, 17th Annual Conference of the International Society for Magnetic Resonance in Medicine, Honolulu, Hawai\'i, April 19-24
Estimation of Static Discrete Choice Models Using Market Level DataNBER
This document discusses methods for estimating static discrete choice models using market-level data rather than individual consumer data. It covers several key topics:
1) The types of market-level and consumer-level data that can be used. Market-level data is easier to obtain but poses challenges for identification and estimation.
2) A common linear random coefficients logit model framework. It includes observed and unobserved product characteristics as well as observed and unobserved consumer heterogeneity.
3) The key challenges of estimating heterogeneity parameters without consumer-level data. It also discusses how to deal with potential endogeneity of unobserved product characteristics.
4) The two-step estimation approach when consumer-level data is available, and
Modeling of Competitive Kinetics of DNA Hybridization Reactionsgantovnik
This document presents a mathematical model for competitive DNA hybridization reactions on microarrays. It introduces competing interactions that can occur, such as specific and non-specific hybridization and intramolecular folding. The model is described through a system of ordinary differential equations considering multiple probe-target interactions and unimolecular folding. Future work to improve the model by including diffusion effects and a parallel solver for large systems is discussed.
The document presents a dynamic discrete choice model of demand for insecticide treated nets (ITNs) that accounts for time inconsistent preferences and unobserved heterogeneity. The model has three periods where agents make ITN purchase and retreatment decisions. Agents are either time consistent, "naive" time inconsistent, or "sophisticated" time inconsistent. The model is identified in two steps - first when types are directly observed using survey responses, and second when types are unobserved. Identification exploits variation from elicited beliefs about malaria risk. The model can point identify time preference parameters and utility functions up to a normalization.
1) The document introduces Bayesian decision theory and its use for statistical pattern classification.
2) It discusses key concepts such as prior and conditional probabilities, loss functions, and deriving the minimum-risk classifier that minimizes expected loss.
3) The minimum-risk classifier chooses the decision or action that minimizes the total risk, calculated from the loss incurred for each state of nature weighted by its posterior probability.
C. Guyon, T. Bouwmans, E. Zahzah, “Foreground detection based on low-rank and block-sparse matrix decomposition”, IEEE International Conference on Image Processing, ICIP 2012, pages 1225-1228, Orlando, Florida, USA, September 2012.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
This document summarizes Chapter 2 of the textbook "Introduction to Analog & Digital Communications" which covers the Fourier representation of signals and systems. The chapter introduces the Fourier transform and its properties, such as how it relates the frequency and time domains. It also defines the Fourier transform mathematically and covers important concepts like the power spectral density and Dirichlet's conditions. Examples of applying the Fourier transform to common signals like rectangular and exponential pulses are also presented.
Initial-Population Bias in the Univariate Estimation of Distribution AlgorithmMartin Pelikan
This document studies the effects of biasing the initial population in the Univariate Marginal Distribution Algorithm (UMDA) on the onemax and noisy onemax problems. Theoretical models are developed to predict the impact on population size, number of generations, and number of evaluations for different levels of initial bias. Experiments match the theoretical predictions, showing that a positively biased initial population improves performance while a negatively biased population harms performance. Introducing noise does not change these effects.
Estimation of Static Discrete Choice Models Using Market Level DataNBER
This document discusses methods for estimating static discrete choice models using market-level data rather than individual consumer data. It covers several key topics:
1) The types of market-level and consumer-level data that can be used. Market-level data is easier to obtain but poses challenges for identification and estimation.
2) A common linear random coefficients logit model framework. It includes observed and unobserved product characteristics as well as observed and unobserved consumer heterogeneity.
3) The key challenges of estimating heterogeneity parameters without consumer-level data. It also discusses how to deal with potential endogeneity of unobserved product characteristics.
4) The two-step estimation approach when consumer-level data is available, and
Modeling of Competitive Kinetics of DNA Hybridization Reactionsgantovnik
This document presents a mathematical model for competitive DNA hybridization reactions on microarrays. It introduces competing interactions that can occur, such as specific and non-specific hybridization and intramolecular folding. The model is described through a system of ordinary differential equations considering multiple probe-target interactions and unimolecular folding. Future work to improve the model by including diffusion effects and a parallel solver for large systems is discussed.
The document presents a dynamic discrete choice model of demand for insecticide treated nets (ITNs) that accounts for time inconsistent preferences and unobserved heterogeneity. The model has three periods where agents make ITN purchase and retreatment decisions. Agents are either time consistent, "naive" time inconsistent, or "sophisticated" time inconsistent. The model is identified in two steps - first when types are directly observed using survey responses, and second when types are unobserved. Identification exploits variation from elicited beliefs about malaria risk. The model can point identify time preference parameters and utility functions up to a normalization.
1) The document introduces Bayesian decision theory and its use for statistical pattern classification.
2) It discusses key concepts such as prior and conditional probabilities, loss functions, and deriving the minimum-risk classifier that minimizes expected loss.
3) The minimum-risk classifier chooses the decision or action that minimizes the total risk, calculated from the loss incurred for each state of nature weighted by its posterior probability.
C. Guyon, T. Bouwmans, E. Zahzah, “Foreground detection based on low-rank and block-sparse matrix decomposition”, IEEE International Conference on Image Processing, ICIP 2012, pages 1225-1228, Orlando, Florida, USA, September 2012.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
This document summarizes Chapter 2 of the textbook "Introduction to Analog & Digital Communications" which covers the Fourier representation of signals and systems. The chapter introduces the Fourier transform and its properties, such as how it relates the frequency and time domains. It also defines the Fourier transform mathematically and covers important concepts like the power spectral density and Dirichlet's conditions. Examples of applying the Fourier transform to common signals like rectangular and exponential pulses are also presented.
Initial-Population Bias in the Univariate Estimation of Distribution AlgorithmMartin Pelikan
This document studies the effects of biasing the initial population in the Univariate Marginal Distribution Algorithm (UMDA) on the onemax and noisy onemax problems. Theoretical models are developed to predict the impact on population size, number of generations, and number of evaluations for different levels of initial bias. Experiments match the theoretical predictions, showing that a positively biased initial population improves performance while a negatively biased population harms performance. Introducing noise does not change these effects.
Lesson 20: Derivatives and the Shapes of Curves (handout)Matthew Leingang
This document contains lecture notes on calculus from a Calculus I course. It covers determining the monotonicity of functions using the first derivative test. Key points include using the sign of the derivative to determine if a function is increasing or decreasing over an interval, and using the first derivative test to classify critical points as local maxima, minima, or neither. Examples are provided to demonstrate finding intervals of monotonicity for various functions and applying the first derivative test.
This document describes a novel statistical damage detection approach using unsupervised support vector machines (SVM). It aims to identify damage in structural components through vibration-based methods. The proposed approach builds a statistical model through unsupervised learning, avoiding the need for measurements from damaged structures. It is computationally efficient even with large numbers of features and does not suffer from local minima problems like artificial neural networks. Numerical simulations show the approach can accurately detect both the occurrence and location of damage.
TUKE MediaEval 2012: Spoken Web Search using DTW and Unsupervised SVMMediaEval2012
This document describes a spoken web search system that uses dynamic time warping (DTW) and an unsupervised support vector machine (SVM). It consists of 3 sections:
1) System architecture - outlines the segmentation, feature extraction, SVM method, and searching algorithm components of the system.
2) Experimental results - provides results from testing the system but no details.
3) Conclusion - the concluding remarks for the system but no specifics are given.
The document discusses projection methods for solving functional equations. Projection methods work by specifying a basis of functions and "projecting" the functional equation against that basis to find the parameters. This allows approximating different objects like decision rules or value functions. The document focuses on spectral methods that use global basis functions and covers various basis options like monomials, trigonometric series, Jacobi polynomials and Chebyshev polynomials. It also discusses how to generalize the basis to multidimensional problems, including using tensor products and Smolyak's algorithm to reduce the number of basis elements.
This document discusses two methods for measuring consumer welfare using demand models: Hausman (1996) and the discrete choice model. Hausman estimates demand for cereal and values the introduction of Apple Cinnamon Cheerios at $78.1 million annually under perfect competition and $66.8 million under imperfect competition. The discrete choice model measures welfare as the inclusive value from a choice set and can value new products by simulating choices with and without them. It is more flexible but still relies on accurate demand estimation.
The document summarizes Miguel Robles' presentation on tools to measure the impact of changes in international food prices on household welfare. It discusses an analytical framework for estimating compensating variation to measure welfare impacts. Empirical estimates are provided for Bangladesh, Pakistan, and Vietnam using household survey data and defining commodity groups. Scenarios analyze observed food price changes between 2006-2008 and a hypothetical 10% price increase. Results show mostly negative welfare impacts, with urban areas and poorer households hurt more. Losses represent a large share of consumption for poorer households.
The document introduces perturbation methods as a way to solve functional equations that describe economic problems. It presents a basic real business cycle model as an example problem that can be solved using perturbation methods. Specifically, it:
1) Defines the real business cycle model as a functional equation system that is difficult to solve directly.
2) Proposes using perturbation methods by introducing a small perturbation parameter (the standard deviation of technology shocks) and solving the problem when this parameter equals zero.
3) Expands the decision rules as Taylor series in terms of the state variables and perturbation parameter to build a local approximation around the deterministic steady state. This leads to a system of equations that can be solved order-by-order for
Reliability-Based Design Optimization Using a Cell Evolution Method ~陳奇中教授演講投影片Chyi-Tsong Chen
The document describes reliability-based design optimization (RBDO) using a cell evolution method. RBDO aims to find optimal designs that satisfy reliability constraints accounting for uncertainties. Traditional RBDO methods are either computationally expensive double-loop approaches or faster single-loop approaches with reduced accuracy. The proposed cell evolution method generates reliability-test cells using genetic algorithms to efficiently and accurately solve RBDO problems. Numerical examples demonstrate the method finds optimal designs matching other approaches but with improved computational efficiency.
The document proposes a new optimization algorithm called the Generalized Baum-Welch (GBW) algorithm for discriminative training on hidden Markov models. GBW is based on Lagrange relaxation of a transformed optimization problem. The Baum-Welch algorithm for maximum likelihood estimation of HMM parameters and the extended Baum-Welch algorithm for discriminative training are both special cases of GBW. The performance of GBW and EBW are compared for a Farsi large vocabulary continuous speech recognition task.
The document discusses methods for solving dynamic stochastic general equilibrium (DSGE) models. It outlines perturbation and projection methods for approximating the solution to DSGE models. Perturbation methods use Taylor series approximations around a steady state to derive linear approximations of the model. Projection methods find parametric functions that best satisfy the model equations. The document also provides an example of applying the implicit function theorem to derive a Taylor series approximation of a policy rule for a neoclassical growth model.
This document provides an introduction and overview of the mathematics textbook. It discusses the importance of mathematics education and outlines the goals and structure of the textbook. The textbook aims to help students learn mathematics fundamentals and apply them to problem solving. It contains 12 chapters covering topics like sets, sequences, algebra, matrices, coordinate geometry, and probability. For each chapter, the document lists the key concepts and learning outcomes. It encourages teachers to facilitate understanding and maximize learning from the textbook.
GECCO'2007: Modeling XCS in Class Imbalances: Population Size and Parameter S...Albert Orriols-Puig
1. The document describes a facetwise analysis of the XCS learning classifier system for class imbalances.
2. It analyzes the population initialization process, generation of rules for minority classes, time to extinction of such rules, and derives a population size bound.
3. The analysis considers problems with multiple classes, one sampled at a lower frequency (minority class), and derives probabilities of sampling instances from each class.
This document provides preparation guidelines for interviews for junior quantitative analyst positions. It recommends spending 40-50% of time reviewing basic math skills like calculus, probability, statistics and financial math. Another 30-40% should be spent programming in C++, focusing on object-oriented principles and data structures. The final 10-20% should cover financial products and modeling. Sample questions test knowledge of derivatives pricing, differential equations, linear algebra, and programming concepts. Problem-solving questions evaluate logical thinking and proof abilities. Overall, the document emphasizes mastering fundamentals before complex topics.
1) The document outlines a teaching plan for quadratic equations and functions over several weeks. It includes learning objectives, outcomes, suggested activities and points to note for teachers.
2) Key concepts covered are quadratic equations, functions, graphs, maximum/minimum values, and solving simultaneous equations. Suggested activities include using graphing calculators, computer software and real-world examples.
3) The document provides detailed guidance for teachers on topics, skills, strategies and values to focus on for each area of learning.
This document summarizes key concepts in nonparametric econometrics and kernel density estimation. It discusses bandwidth selection methods like cross-validation and plug-in approaches. It also covers multivariate density estimation, noting the trade-off between bias and variance. The document analyzes a real example from DiNardo and Tobias on estimating the density of female wages.
The document discusses three examples of nonlinear and non-Gaussian DSGE models. The first example features Epstein-Zin preferences to allow for a separation between risk aversion and the intertemporal elasticity of substitution. The second example models volatility shocks using time-varying variances. The third example aims to distinguish between the effects of stochastic volatility ("fortune") versus parameter drifting ("virtue") in explaining time-varying volatility in macroeconomic variables. The document outlines the motivation, structure, and solution methods for these three nonlinear DSGE models.
This document discusses filtering and likelihood inference. It begins by introducing filtering problems in economics, such as evaluating DSGE models. It then presents the state space representation approach, which models the transition and measurement equations with stochastic shocks. The goal of filtering is to compute the conditional densities of states given observed data over time using tools like the Chapman-Kolmogorov equation and Bayes' theorem. Filtering provides a recursive way to make predictions and updates estimates as new data arrives.
This document is the preface to a book on computer science theory. It provides an overview of the book's contents, which include deterministic and non-deterministic finite automata, context-free grammars, pushdown automata, Turing machines, computability, and complexity theory. It thanks various individuals for their support and encouragement during the writing process. It invites readers to provide suggestions to improve the book.
This document presents a new iterative method called the Parametric Method of Iteration for solving nonlinear systems of equations. The method rewrites each equation using a set of positive parameters and iterates the solutions until convergence within a desired accuracy. The method converges faster than traditional iteration and Newton-Raphson methods, as shown through examples. The parametric method generalizes the existing methods and allows tuning of parameters to accelerate convergence for different types of equations.
This document discusses tuning hyperparameters using cross validation. It begins by motivating the need for model selection to choose hyperparameters that provide a good balance between model complexity and accuracy. It then discusses assessing model quality using measures like error rate from a test set. Cross validation techniques like k-fold and leave-one-out are presented as methods for estimating accuracy without using all the data for training. The document concludes by discussing strategies for implementing model selection like using grids to search hyperparameters and evaluating results.
The document presents a study that uses machine learning techniques to build a diagnostic model to distinguish between very mild dementia (VMD) and cognitively normal individuals using MRI data. Seven machine learning algorithms were tested including naive Bayes, Bayesian networks, decision trees, support vector machines, and neural networks. The right hippocampus was the most important discriminating brain region. Algorithms like naive Bayes and support vector machines performed better than previous statistical approaches at classifying VMD versus controls based on MRI data. Cross-validation is a more reliable performance measure than accuracy alone.
Lesson 20: Derivatives and the Shapes of Curves (handout)Matthew Leingang
This document contains lecture notes on calculus from a Calculus I course. It covers determining the monotonicity of functions using the first derivative test. Key points include using the sign of the derivative to determine if a function is increasing or decreasing over an interval, and using the first derivative test to classify critical points as local maxima, minima, or neither. Examples are provided to demonstrate finding intervals of monotonicity for various functions and applying the first derivative test.
This document describes a novel statistical damage detection approach using unsupervised support vector machines (SVM). It aims to identify damage in structural components through vibration-based methods. The proposed approach builds a statistical model through unsupervised learning, avoiding the need for measurements from damaged structures. It is computationally efficient even with large numbers of features and does not suffer from local minima problems like artificial neural networks. Numerical simulations show the approach can accurately detect both the occurrence and location of damage.
TUKE MediaEval 2012: Spoken Web Search using DTW and Unsupervised SVMMediaEval2012
This document describes a spoken web search system that uses dynamic time warping (DTW) and an unsupervised support vector machine (SVM). It consists of 3 sections:
1) System architecture - outlines the segmentation, feature extraction, SVM method, and searching algorithm components of the system.
2) Experimental results - provides results from testing the system but no details.
3) Conclusion - the concluding remarks for the system but no specifics are given.
The document discusses projection methods for solving functional equations. Projection methods work by specifying a basis of functions and "projecting" the functional equation against that basis to find the parameters. This allows approximating different objects like decision rules or value functions. The document focuses on spectral methods that use global basis functions and covers various basis options like monomials, trigonometric series, Jacobi polynomials and Chebyshev polynomials. It also discusses how to generalize the basis to multidimensional problems, including using tensor products and Smolyak's algorithm to reduce the number of basis elements.
This document discusses two methods for measuring consumer welfare using demand models: Hausman (1996) and the discrete choice model. Hausman estimates demand for cereal and values the introduction of Apple Cinnamon Cheerios at $78.1 million annually under perfect competition and $66.8 million under imperfect competition. The discrete choice model measures welfare as the inclusive value from a choice set and can value new products by simulating choices with and without them. It is more flexible but still relies on accurate demand estimation.
The document summarizes Miguel Robles' presentation on tools to measure the impact of changes in international food prices on household welfare. It discusses an analytical framework for estimating compensating variation to measure welfare impacts. Empirical estimates are provided for Bangladesh, Pakistan, and Vietnam using household survey data and defining commodity groups. Scenarios analyze observed food price changes between 2006-2008 and a hypothetical 10% price increase. Results show mostly negative welfare impacts, with urban areas and poorer households hurt more. Losses represent a large share of consumption for poorer households.
The document introduces perturbation methods as a way to solve functional equations that describe economic problems. It presents a basic real business cycle model as an example problem that can be solved using perturbation methods. Specifically, it:
1) Defines the real business cycle model as a functional equation system that is difficult to solve directly.
2) Proposes using perturbation methods by introducing a small perturbation parameter (the standard deviation of technology shocks) and solving the problem when this parameter equals zero.
3) Expands the decision rules as Taylor series in terms of the state variables and perturbation parameter to build a local approximation around the deterministic steady state. This leads to a system of equations that can be solved order-by-order for
Reliability-Based Design Optimization Using a Cell Evolution Method ~陳奇中教授演講投影片Chyi-Tsong Chen
The document describes reliability-based design optimization (RBDO) using a cell evolution method. RBDO aims to find optimal designs that satisfy reliability constraints accounting for uncertainties. Traditional RBDO methods are either computationally expensive double-loop approaches or faster single-loop approaches with reduced accuracy. The proposed cell evolution method generates reliability-test cells using genetic algorithms to efficiently and accurately solve RBDO problems. Numerical examples demonstrate the method finds optimal designs matching other approaches but with improved computational efficiency.
The document proposes a new optimization algorithm called the Generalized Baum-Welch (GBW) algorithm for discriminative training on hidden Markov models. GBW is based on Lagrange relaxation of a transformed optimization problem. The Baum-Welch algorithm for maximum likelihood estimation of HMM parameters and the extended Baum-Welch algorithm for discriminative training are both special cases of GBW. The performance of GBW and EBW are compared for a Farsi large vocabulary continuous speech recognition task.
The document discusses methods for solving dynamic stochastic general equilibrium (DSGE) models. It outlines perturbation and projection methods for approximating the solution to DSGE models. Perturbation methods use Taylor series approximations around a steady state to derive linear approximations of the model. Projection methods find parametric functions that best satisfy the model equations. The document also provides an example of applying the implicit function theorem to derive a Taylor series approximation of a policy rule for a neoclassical growth model.
This document provides an introduction and overview of the mathematics textbook. It discusses the importance of mathematics education and outlines the goals and structure of the textbook. The textbook aims to help students learn mathematics fundamentals and apply them to problem solving. It contains 12 chapters covering topics like sets, sequences, algebra, matrices, coordinate geometry, and probability. For each chapter, the document lists the key concepts and learning outcomes. It encourages teachers to facilitate understanding and maximize learning from the textbook.
GECCO'2007: Modeling XCS in Class Imbalances: Population Size and Parameter S...Albert Orriols-Puig
1. The document describes a facetwise analysis of the XCS learning classifier system for class imbalances.
2. It analyzes the population initialization process, generation of rules for minority classes, time to extinction of such rules, and derives a population size bound.
3. The analysis considers problems with multiple classes, one sampled at a lower frequency (minority class), and derives probabilities of sampling instances from each class.
This document provides preparation guidelines for interviews for junior quantitative analyst positions. It recommends spending 40-50% of time reviewing basic math skills like calculus, probability, statistics and financial math. Another 30-40% should be spent programming in C++, focusing on object-oriented principles and data structures. The final 10-20% should cover financial products and modeling. Sample questions test knowledge of derivatives pricing, differential equations, linear algebra, and programming concepts. Problem-solving questions evaluate logical thinking and proof abilities. Overall, the document emphasizes mastering fundamentals before complex topics.
1) The document outlines a teaching plan for quadratic equations and functions over several weeks. It includes learning objectives, outcomes, suggested activities and points to note for teachers.
2) Key concepts covered are quadratic equations, functions, graphs, maximum/minimum values, and solving simultaneous equations. Suggested activities include using graphing calculators, computer software and real-world examples.
3) The document provides detailed guidance for teachers on topics, skills, strategies and values to focus on for each area of learning.
This document summarizes key concepts in nonparametric econometrics and kernel density estimation. It discusses bandwidth selection methods like cross-validation and plug-in approaches. It also covers multivariate density estimation, noting the trade-off between bias and variance. The document analyzes a real example from DiNardo and Tobias on estimating the density of female wages.
The document discusses three examples of nonlinear and non-Gaussian DSGE models. The first example features Epstein-Zin preferences to allow for a separation between risk aversion and the intertemporal elasticity of substitution. The second example models volatility shocks using time-varying variances. The third example aims to distinguish between the effects of stochastic volatility ("fortune") versus parameter drifting ("virtue") in explaining time-varying volatility in macroeconomic variables. The document outlines the motivation, structure, and solution methods for these three nonlinear DSGE models.
This document discusses filtering and likelihood inference. It begins by introducing filtering problems in economics, such as evaluating DSGE models. It then presents the state space representation approach, which models the transition and measurement equations with stochastic shocks. The goal of filtering is to compute the conditional densities of states given observed data over time using tools like the Chapman-Kolmogorov equation and Bayes' theorem. Filtering provides a recursive way to make predictions and updates estimates as new data arrives.
This document is the preface to a book on computer science theory. It provides an overview of the book's contents, which include deterministic and non-deterministic finite automata, context-free grammars, pushdown automata, Turing machines, computability, and complexity theory. It thanks various individuals for their support and encouragement during the writing process. It invites readers to provide suggestions to improve the book.
This document presents a new iterative method called the Parametric Method of Iteration for solving nonlinear systems of equations. The method rewrites each equation using a set of positive parameters and iterates the solutions until convergence within a desired accuracy. The method converges faster than traditional iteration and Newton-Raphson methods, as shown through examples. The parametric method generalizes the existing methods and allows tuning of parameters to accelerate convergence for different types of equations.
This document discusses tuning hyperparameters using cross validation. It begins by motivating the need for model selection to choose hyperparameters that provide a good balance between model complexity and accuracy. It then discusses assessing model quality using measures like error rate from a test set. Cross validation techniques like k-fold and leave-one-out are presented as methods for estimating accuracy without using all the data for training. The document concludes by discussing strategies for implementing model selection like using grids to search hyperparameters and evaluating results.
The document presents a study that uses machine learning techniques to build a diagnostic model to distinguish between very mild dementia (VMD) and cognitively normal individuals using MRI data. Seven machine learning algorithms were tested including naive Bayes, Bayesian networks, decision trees, support vector machines, and neural networks. The right hippocampus was the most important discriminating brain region. Algorithms like naive Bayes and support vector machines performed better than previous statistical approaches at classifying VMD versus controls based on MRI data. Cross-validation is a more reliable performance measure than accuracy alone.
This document provides a practical guide for using support vector machines (SVMs) for classification tasks. It recommends beginners follow a simple procedure: 1) preprocess data by converting categorical features to numeric and scaling attributes, 2) use a radial basis function kernel, 3) perform cross-validation to select optimal values for hyperparameters C and γ, and 4) train the full model on the training set using the best hyperparameters. The guide explains why this procedure often provides reasonable results for novices and illustrates it using examples of real-world classification problems.
This document proposes a simple procedure for beginners to obtain reasonable results when using support vector machines (SVMs) for classification tasks. The procedure involves preprocessing data through scaling, using a radial basis function kernel, selecting model parameters through cross-validation grid search, and training the full model on the preprocessed data. The document provides examples applying this procedure to real-world datasets, demonstrating improved accuracy over approaches without careful preprocessing and parameter selection.
This document discusses classifier performance evaluation. It covers the following key points in 3 sentences:
The document outlines different methods for evaluating classifier performance, including hold out, k-fold cross validation, and bootstrap aggregating. It emphasizes that evaluation should be treated as statistical hypothesis testing using metrics like accuracy, precision, and recall calculated from a confusion matrix. Proper evaluation also requires partitioning data into separate training and test sets to avoid overfitting and get an accurate estimate of a classifier's generalization performance.
The document discusses machine learning techniques for multivariate data analysis using the TMVA toolkit. It describes several common classification problems in high energy physics (HEP) and summarizes several machine learning algorithms implemented in TMVA for supervised learning, including rectangular cut optimization, likelihood methods, neural networks, boosted decision trees, support vector machines and rule ensembles. It also discusses challenges like nonlinear correlations between input variables and techniques for data preprocessing and decorrelation.
Analytical study of feature extraction techniques in opinion miningcsandit
Although opinion mining is in a nascent stage of development but still the ground is set for
dense growth of researches in the field. One of the important activities of opinion mining is to
extract opinions of people based on characteristics of the object under study. Feature extraction
in opinion mining can be done by various ways like that of clustering, support vector machines
etc. This paper is an attempt to appraise the various techniques of feature extraction. The first
part discusses various techniques and second part makes a detailed appraisal of the major
techniques used for feature extraction
ANALYTICAL STUDY OF FEATURE EXTRACTION TECHNIQUES IN OPINION MININGcsandit
Although opinion mining is in a nascent stage of development but still the ground is set for dense growth of researches in the field. One of the important activities of opinion mining is to extract opinions of people based on characteristics of the object under study. Feature extraction in opinion mining can be done by various ways like that of clustering, support vector machines
etc. This paper is an attempt to appraise the various techniques of feature extraction. The first part discusses various techniques and second part makes a detailed appraisal of the major techniques used for feature extraction
Radial Basis Function Neural Network (RBFNN), Induction Motor, Vector control...cscpconf
Although opinion mining is in a nascent stage of development but still the ground is set for dense growth of researches in the field. One of the important activities of opinion mining is to
extract opinions of people based on characteristics of the object under study. Feature extraction in opinion mining can be done by various ways like that of clustering, support vector machines
etc. This paper is an attempt to appraise the various techniques of feature extraction. The first part discusses various techniques and second part makes a detailed appraisal of the major techniques used for feature extraction.
Anomaly detection using deep one class classifier홍배 김
The document discusses anomaly detection techniques using deep one-class classifiers and generative adversarial networks (GANs). It proposes using an autoencoder to extract features from normal images, training a GAN on those features to model the distribution, and using a one-class support vector machine (SVM) to determine if new images are within the normal distribution. The method detects and localizes anomalies by generating a binary mask for abnormal regions. It also discusses Gaussian mixture models and the expectation-maximization algorithm for modeling multiple distributions in data.
Item Response Theory in Constructing MeasuresCarlo Magno
The document discusses approaches to analyzing test data, including classical test theory (CTT) and item response theory (IRT). It provides an overview of CTT, limitations of CTT, approaches in IRT including advantages over CTT. It also discusses the Rasch model as an example of an IRT model. The document outlines what can be interpreted from IRT analyses including using IRT for scales. It concludes by mentioning some applications of IRT on tests.
This document discusses the identification of bacterial exotoxins and the use of support vector machines for classification. It notes that exotoxin identification is important for understanding disease mechanisms and developing treatments. It then provides an overview of support vector machines, including how they find the optimal separating hyperplane between classes using kernels to project data into higher dimensions. The rest of the document details how the author collected toxin and non-toxin protein sequences, extracted physicochemical features, trained an SVM model using LIBSVM tools, and evaluated performance, achieving over 90% accuracy.
This document discusses computer aided detection (CAD) of abnormalities in medical images. It begins by outlining CAD and some of the key machine learning challenges, including correlated training data, non-standard evaluation metrics, runtime constraints, lack of objective ground truths, and data shortages. It then describes solutions like multiple instance learning, batch classification, cascaded classifiers, crowdsourcing algorithms, and multi-task learning. The document concludes by reviewing the clinical impact of CAD systems through several independent studies, which demonstrated improved radiologist performance and sensitivity in detecting diseases.
This document provides an introduction to machine learning, covering key topics such as what machine learning is, common learning algorithms and applications. It discusses linear models, kernel methods, neural networks, decision trees and more. It also addresses challenges in machine learning like balancing fit and robustness, and evaluating model performance using techniques like ROC curves. The goal of machine learning is to build models that can learn from data to make predictions or decisions.
This document provides a practical guide for using support vector machines (SVMs) for classification tasks. It recommends beginners follow a simple procedure of transforming data, scaling it, using a radial basis function kernel, and performing cross-validation to select hyperparameters. Real-world examples show this procedure achieves better accuracy than approaches without these steps. The guide aims to help novices rapidly obtain acceptable SVM results without a deep understanding of the underlying theory.
Surface features with nonparametric machine learningSylvain Ferrandiz
For data savvy users (analysts, scientists, ops, engineers) who are willing to discover some nonparametric machine learning algos that might help while competing via Kaggle or, more down-to-earth-ly, while having not that much time to spend on some predictive analytics projects. Talk given at Paris Kaggle meetup.
This document discusses various methods for evaluating and improving the accuracy of classification models, including:
- Confusion matrices and measures like accuracy, sensitivity, and precision to evaluate classifier performance.
- Ensemble methods like bagging and boosting that combine multiple models to improve accuracy. Bagging averages predictions from models trained on bootstrap samples, while boosting gives higher weight to instances harder to classify.
- Model selection techniques like statistical tests and ROC curves to compare models and determine the best performing one. ROC curves show the tradeoff between true and false positives for threshold-based classifiers.
This document provides an overview of machine learning techniques for classification and anomaly detection. It begins with an introduction to machine learning and common tasks like classification, clustering, and anomaly detection. Basic classification techniques are then discussed, including probabilistic classifiers like Naive Bayes, decision trees, instance-based learning like k-nearest neighbors, and linear classifiers like logistic regression. The document provides examples and comparisons of these different methods. It concludes by discussing anomaly detection and how it differs from classification problems, noting challenges like having few positive examples of anomalies.
- A high-level overview of artificial intelligence
- The importance of predictions across different domains of life
- Big (text) data
- Competition as a discovery process
- Domain-general learning
- Computer vision and natural language processing
- Elements of a machine learning system
- A hierarchy of problem classes
- Data collection
- The purpose of a model
- Logistic loss function
- Likelihood, log likelihood and maximum likelihood
- Ockham's Razor
- Intelligence as sequence prediction
- Building blocks of neural networks: neurons, weights and layers
- Logistic regression as a neural network
- Sigmoid function
- A look at backpropagation
- Gradient descent
- Convolutional neural networks
- Max-pooling
- Deep neural networks
2. Declaration of Conflict of Interest or
Relationship
Speaker Name: Brandon Whitcher
I have the following conflict of interest to disclose with regard to
the subject matter of this presentation:
Company name: GlaxoSmithKline
Type of relationship: Employment
3. Outline
Motivation
– Univariate vs. multivariate
data
Supervised Learning
– Linear methods
Regression
Classification
– Separating hyperplanes
– Support vector machine
(SVM)
Examples
– Tuning
– Cross-validation
– Visualization
– Receiver operating
characteristics (ROC)
Conclusions
4. Motivation
Imaging trials rarely produce a single measurement.
– Demographic
– Questionnaire
– Genetic
– Serum biomarkers
– Structural and functional imaging biomarkers
Imaging biomarkers
– Multiple measurements occur within or between modalities
MRI, PET, CT, etc.
– Functional imaging:
Diffusion-weighted imaging DWI
Dynamic contrast-enhanced MRI DCE-MRI
Dynamic susceptibility contrast-enhanced MRI DSC-MRI
Blood oxygenation level dependent MRI BOLD-MRI
MR spectroscopy MRS
How can we combine these disparate sources of information?
What new questions can be addressed?
5. Neuroscience Example
Fig. 1. Voxel-based-morphometry (VBM) analysis showing an additive effect of the APOE ε4
allele (APOE4) on grey matter volume (GMV).
Filippini et al. NeuroImage 2008
7. What is Supervised Learning?
T1, T2, DWI, Regression,
DCE-MRI, LDA, SVM,
MRS, Genetics
Test Data
NN
Step 2
Training Supervised
Model
Data Learning
Step 1
Benign, Results
malignant
8. Linear Regression
Given a set of inputs X = (X1, X2, …, Xp), want to predict Y
– Linear regression model: f(X) = β0 + ∑j Xjβj
– Minimize residual sum of squares: RSS(β) = ∑i (yi – f(xi))2
9. Linear Methods for Classification
Linear Discriminant Analysis (LDA)
– Procedure:
Estimate mean vectors and covariance matrix
Calculate linear decision boundaries
Classify points using linear decision boundaries
Logistic regression is another popular method
– Binary outcome with qualitative/quantitative predictors
– Maximize likelihood via iteratively re-weighted least squares
Neither method was designed to explicitly separate data.
– LDA = optimized when mean vector and covariance is known
– Logistic regression = to understand the role of the input variables
10. LDA w/ Two Classes: Step-by-Step
Measurement #2
Measurement #1
11. LDA w/ Three Classes: Step-by-Step
Measuring #2
Measurement #1
12. Separating Hyperplanes
Rosenblatt’s Perceptron Learning Algorithm (1958)
– Minimizes the distance of misclassified points to the decision
boundary:
min D(β,β0) = –∑iєM yi(xTβ + β0); yi = ±1
– Converges in a “finite” number of steps.
Problems (Ripley, 1996)
1. Separable data implies many solutions (initial conditions).
2. Slow convergence... smaller the gap = longer the time.
3. Nonseparable data implies the algorithm will not converge!
Optimal separating hyperplanes (Vapnik and Chervonenkis, 1963)
– Forms the foundation for support vector machines.
14. Support Vector Machines (Vapnik 1996)
Separates two classes and maximizes the distance to the closest point
from either class:
max C subject to yi(xTβ + β0) ≥ C; yi = ±1
Extends “optimal separating hyperplanes”
– Nonseparable case and nonlinear boundaries
– Contain a “cost” parameter that may be optimized
– May be used in the regression setting
Basis expansions
– Enlarges the feature space
– Allowed to get very large or infinite
– Examples include k(x,x′) = exp(-γ║x-x′║2); γ > 0
Gaussian radial basis function (RBF) kernel
Polynomial kernel
ANOVA radial basis kernel
– Contain a “scaling factor” that may be optimized
15. Support Vector Classifiers: separable case
1
C
1 margin
C
support point
Adapted from Hastie, Tibshirani and Friedman (2001)
xT 0 0
16. Support Vector Classifiers: nonseparable case
1
C
1 margin
C
4
5
1
3
2
Adapted from Hastie, Tibshirani and Friedman (2001)
xT 0 0
26. Example: Prostate Specific Antigen (PSA)
Stamey et al. (1989); used in Hastie, Tibshirani and Friedman (2001).
Correlation between the level of PSA and various clinical measures (N = 97)
– log cancer volume,
– log prostate weight,
– log of BPH amount,
– seminal vesicle invasion,
– log of capsular penetration,
– Gleason score, and
– percent of Gleason scores 4 or 5.
Regression problem since outcome measure is quantitative.
Training data = 67, Test data = 30.
32. Conclusions
Multivariate data are being collected from imaging studies.
In order to utilize this information:
– Use the “right” statistical method
– Collaborate with quantitative scientists
– Paradigm shift in the analysis of imaging studies
Embrace the richness of multi-functional imaging data
– Quantitative
– Raw (avoid summaries)
Design of imaging studies requires
– A priori knowledge
– Few and focused scientific questions
– Well-defined methodology
34. Bibliography
Filippini N, Rao, A, et al. Anatomically-distinct genetic associations of APOE ε4 allele
load with regional cortical atrophy in Alzheimer's disease. NeuroImage 2009, 44:724-
728.
Freer TW, Ulissey, MJ. Screening Mammography with Computer-aided Detection:
Prospective Study of 12,860 Patients in a Community Breast Center. Radiology 2001,
220:781-786.
Hastie T, Tibshirani, R, Freidman, J. The Elements of Statistical Learning, Springer,
2001.
McDonough KL. Breast Cancer Stage Cost Analysis in a Manage Care Population.
American Journal of Managed Care 1999, 5(6):S377-S382.
R Development Team. R: A Language and Environment for Statistical Computing. R
Foundation for Statistical Computing, Vienna, Austria.
– www.R-project.org
– R package e1071
– R package mlbench
Ripley, BD. Pattern Recognition and Neural Networks, Cambridge University Press,
1996.
Vos PC, Hambrock, T, et al. Computerized analysis of prostate lesions in the peripheral
zone using dynamic contrast enhanced MRI. Medical Physics 2008, 35(3):888-899.
Wolberg WH, Mangasarian, OL. Multisurface method of pattern separation for medical
diagnosis applied to breast cytology. PNAS 1990, 87(23):9193-9196.