AdaBoost is an ensemble learning algorithm that combines multiple weak learners into a single strong learner. It works in rounds, assigning higher weights to examples that previous rounds misclassified. Each weak learner is trained on the reweighted data and must only be slightly better than random guessing. AdaBoost then calculates error rates and weights and combines predictions from all weak learners into a final strong learner using a weighted majority vote. The algorithm stops when error rate stops decreasing or the maximum number of rounds is reached.
The document is a mid-semester exam for a signals, systems and controls course containing 6 questions testing various concepts in continuous and discrete time signals and linear time-invariant systems. The questions cover topics such as linearity properties, time shifting and time reversal, Fourier series representation of signals, Fourier transform properties, convolution, frequency response and impulse response of LTI systems.
The document describes a Hamiltonian with terms including Ji,j|ωiωj| and Ei|ωiωi| that depends on parameters ∆/J and ω. It studies the behavior of the system as ∆/J increases from 0 to greater than 6, including plots of the momentum distribution |P(k)|2 that show it spreading out over more values of k/k1. The dependence of the system on other parameters like α, s1, and s2 is also examined through additional plots.
1) The document outlines the nonlinear equilibrium conditions of a simple New Keynesian model without capital. It discusses formulating the model's nonlinear equations to study optimal monetary policy and higher-order solutions.
2) It presents the key components of the model, including household and firm behavior assumptions. Households maximize utility from consumption and labor. Firms set prices according to Calvo pricing and maximize profits.
3) The document derives the nonlinear equilibrium conditions that characterize household and firm optimization, including the household's intertemporal FOC and the intermediate firm's price-setting problem. It expresses the model's equilibrium objects like marginal costs and the price index.
This document discusses unconditionally stable finite-difference time-domain (FDTD) methods for solving Maxwell's equations numerically. It outlines FDTD algorithms such as Yee's method from 1966 which discretize the equations on a staggered grid. It also discusses the von Neumann stability analysis and compares implicit Crank-Nicolson and alternating-direction implicit methods to conventional explicit FDTD methods. The document notes the advantages of unconditionally stable methods but also mentions potential disadvantages.
The document summarizes two models:
1. The Lo-Zivot Threshold Cointegration Model, which uses a threshold vector error correction model (TVECM) to analyze the dynamic adjustment of cointegrated time series variables to their long-run equilibrium. It allows for nonlinear and asymmetric adjustment speeds.
2. A bivariate vector error correction model (VECM) and band-threshold vector error correction model (BAND-TVECM) that extend the VECM to allow for nonlinear and discontinuous adjustments to long-run equilibrium across multiple regimes defined by thresholds on a variable. This captures asymmetric adjustment speeds and dynamic behavior.
The BAND-TVECM allows modeling of
Cosmin Crucean: Perturbative QED on de Sitter Universe.SEENET-MTP
The document summarizes key aspects of quantum field theory on de Sitter spacetime, including solutions to the Dirac, scalar, electromagnetic, and other field equations. It presents:
1) Fundamental solutions for the Dirac equation and orthonormalization relations for Dirac spinor modes.
2) Solutions to the Klein-Gordon equation for a scalar field and corresponding orthonormalization relations.
3) Quantization of electromagnetic vector potentials in the Coulomb gauge and orthonormalization relations for photon modes.
The document outlines research on developing optimal finite difference grids for solving elliptic and parabolic partial differential equations (PDEs). It introduces the motivation to accurately compute Neumann-to-Dirichlet (NtD) maps. It then summarizes the formulation and discretization of model elliptic and parabolic PDE problems, including deriving the discrete NtD map. It presents results on optimal grid design and the spectral accuracy achieved. Future work is proposed on extending the NtD map approach to non-uniformly spaced boundary data.
The document is a mid-semester exam for a signals, systems and controls course containing 6 questions testing various concepts in continuous and discrete time signals and linear time-invariant systems. The questions cover topics such as linearity properties, time shifting and time reversal, Fourier series representation of signals, Fourier transform properties, convolution, frequency response and impulse response of LTI systems.
The document describes a Hamiltonian with terms including Ji,j|ωiωj| and Ei|ωiωi| that depends on parameters ∆/J and ω. It studies the behavior of the system as ∆/J increases from 0 to greater than 6, including plots of the momentum distribution |P(k)|2 that show it spreading out over more values of k/k1. The dependence of the system on other parameters like α, s1, and s2 is also examined through additional plots.
1) The document outlines the nonlinear equilibrium conditions of a simple New Keynesian model without capital. It discusses formulating the model's nonlinear equations to study optimal monetary policy and higher-order solutions.
2) It presents the key components of the model, including household and firm behavior assumptions. Households maximize utility from consumption and labor. Firms set prices according to Calvo pricing and maximize profits.
3) The document derives the nonlinear equilibrium conditions that characterize household and firm optimization, including the household's intertemporal FOC and the intermediate firm's price-setting problem. It expresses the model's equilibrium objects like marginal costs and the price index.
This document discusses unconditionally stable finite-difference time-domain (FDTD) methods for solving Maxwell's equations numerically. It outlines FDTD algorithms such as Yee's method from 1966 which discretize the equations on a staggered grid. It also discusses the von Neumann stability analysis and compares implicit Crank-Nicolson and alternating-direction implicit methods to conventional explicit FDTD methods. The document notes the advantages of unconditionally stable methods but also mentions potential disadvantages.
The document summarizes two models:
1. The Lo-Zivot Threshold Cointegration Model, which uses a threshold vector error correction model (TVECM) to analyze the dynamic adjustment of cointegrated time series variables to their long-run equilibrium. It allows for nonlinear and asymmetric adjustment speeds.
2. A bivariate vector error correction model (VECM) and band-threshold vector error correction model (BAND-TVECM) that extend the VECM to allow for nonlinear and discontinuous adjustments to long-run equilibrium across multiple regimes defined by thresholds on a variable. This captures asymmetric adjustment speeds and dynamic behavior.
The BAND-TVECM allows modeling of
Cosmin Crucean: Perturbative QED on de Sitter Universe.SEENET-MTP
The document summarizes key aspects of quantum field theory on de Sitter spacetime, including solutions to the Dirac, scalar, electromagnetic, and other field equations. It presents:
1) Fundamental solutions for the Dirac equation and orthonormalization relations for Dirac spinor modes.
2) Solutions to the Klein-Gordon equation for a scalar field and corresponding orthonormalization relations.
3) Quantization of electromagnetic vector potentials in the Coulomb gauge and orthonormalization relations for photon modes.
The document outlines research on developing optimal finite difference grids for solving elliptic and parabolic partial differential equations (PDEs). It introduces the motivation to accurately compute Neumann-to-Dirichlet (NtD) maps. It then summarizes the formulation and discretization of model elliptic and parabolic PDE problems, including deriving the discrete NtD map. It presents results on optimal grid design and the spectral accuracy achieved. Future work is proposed on extending the NtD map approach to non-uniformly spaced boundary data.
This document contains mathematical equations and definitions related to quantum mechanics and quantum operators. It defines operators such as momentum, position, angular momentum, and their commutation relations. It also provides equations for wave functions, energy levels, and harmonic oscillator states. Harmonic oscillator wave functions, energy eigenvalues, and operator relations are summarized.
The document discusses modeling decision making deficits in disorders that impact the frontostriatal system using computational models of reinforcement learning. It notes that many such disorders involve changes in motivation and some have genetic heritability. However, the effects of candidate genes are generally small. The author proposes using a theoretical model of reinforcement learning that incorporates data on dopamine prediction errors and the basal ganglia to help identify which genes, tasks, and measures are most relevant. The model aims to integrate findings on how dopamine affects striatal learning of positive and negative prediction errors. Data from a temporal decision making task is presented that the model can fit at both group and single subject levels. The model may help modulate reinforcement learning parameters based on neurogenetic and pharmacological
Asset Prices in Segmented and Integrated Marketsguasoni
This document summarizes a model of asset pricing in segmented and integrated markets. It begins with motivation from the financialization of commodities and market integration. It then presents a model with two regions/trees producing dividends. Equilibria are characterized for when the regions are segmented and integrated. Key results include asset prices being more cyclical and negatively correlated in segmentation, but highly positively correlated in integration. Integration always increases welfare even if it sometimes lowers asset prices and total wealth. Both regions would choose integration to access a smoother consumption stream.
This document summarizes a presentation on numerically solving spatiotemporal models from ecology by implementing an implicit finite difference method in C++. It discusses classical population dynamics models, extending these to include continuous spatial position by using reaction-diffusion systems. It describes discretizing the domain and deriving finite-difference schemes, then solving the equations using GMRES with an ILU preconditioner. Questions addressed include convergence rates and modeling plankton dynamics.
This document summarizes selection algorithms and the 1-center problem.
The selection algorithm uses a prune and search approach. It recursively partitions the dataset into subsets based on the median, pruning away elements that are guaranteed to be outside the desired rank. This results in a linear time complexity of O(n).
The 1-center problem finds the smallest circle enclosing a set of points. A constrained version restricts the center to a given line. The algorithm works by forming point pairs, computing bisectors, and recursively pruning points outside the optimal region.
By tracking the sign of distances to farthest points, the full 2D solution can also be obtained in linear time by recursively considering constrained subproblems on the x
This document describes a collapsed dynamic factor analysis model for macroeconomic forecasting. It summarizes that multivariate time series models can more accurately capture relationships between economic variables compared to univariate models. The document then presents a collapsed dynamic factor model that relates a target time series (yt) to unobserved dynamic factors (Ft) estimated from related macroeconomic data (gt). Out-of-sample forecasting experiments on US personal income and industrial production data demonstrate the model achieves more accurate point forecasts than univariate benchmarks like random walk or AR(2) models.
The document describes 17 Prolog functions for working with lists:
1. member/2 - Checks if an element is a member of a list.
2. mylength/2 - Calculates the length of a list.
3. myappend/3 - Appends two lists together.
4. replace/3 - Replaces all instances of an element with a new value in a list.
5. Various other functions for manipulating lists like reversing, inserting, deleting elements, counting occurrences, etc.
This paper models competition between multiple market makers and analyzes how increasing the number of market makers affects transaction costs for liquidity traders. It finds that:
1) There is no pure strategy equilibrium, but there exists a mixed strategy equilibrium where each market maker randomly sets prices between μ and 1.
2) Increasing the number of market makers increases transaction costs, counter to the traditional view that more competition reduces costs.
3) With elastic demand, the competitive equilibrium price rises to meet demand, but trading still occurs with positive probability as the elasticity approaches zero.
This document introduces ∞-tuples of bounded linear operators on a Banach space and conditions for an ∞-tuple to satisfy the Hypercyclicity Criterion. It defines key concepts such as hypercyclic and semi-periodic vectors. Several theorems are presented: the Hypercyclicity Criterion for ∞-Tuples provides sufficient conditions for an ∞-tuple to be hypercyclic; if an ∞-tuple satisfies these conditions and has a subset of semi-periodic vectors, then it satisfies the Hypercyclicity Criterion; and if an ∞-tuple is hypercyclic with a dense generalized kernel, then it satisfies the Hypercyclicity Criterion. The
This document describes a clustering procedure and nonparametric mixture estimation. It introduces a mixture density model where the goal is to efficiently estimate the mixture weights (αi) and component densities (fi). A two-stage clustering algorithm is proposed: 1) perform clustering on covariates (X) to estimate labels (Ik), and 2) estimate component densities (fi) using kernel density estimation within each cluster. The performance of this approach depends on the clustering method's misclassification error. A toy example with two components having disjoint support densities for X is provided to illustrate the model.
The document discusses Gauss-Seidel, Successive Over Relaxation (SOR), and block SOR methods for solving systems of linear equations. Gauss-Seidel converges faster than Jacobi iteration. SOR can further accelerate convergence by introducing a relaxation parameter ω between 0 and 2. Block SOR generalizes the approach to block-structured matrices by solving blocks simultaneously. Examples show how to apply these methods to finite difference discretizations in 2D and 3D.
This document contains a chapter on integration with 20 exercises involving calculating areas under curves. The exercises provide functions defining regions and ask the reader to calculate areas using various techniques like right endpoints, left endpoints, and trapezoid rules. The functions include polynomials, trigonometric functions, exponentials, and logarithms. Calculating areas allows practicing applying definitions of integrals to find anti-derivatives and definite integrals.
04 structured prediction and energy minimization part 1zukun
The document discusses structured prediction problems and energy minimization approaches. It describes how structured prediction involves finding the optimal prediction y* from a set of possibilities Y that maximizes an objective function g(x,y). Exactly solving such problems is difficult because Y is large but finite. The document outlines desirable properties for algorithms that evaluate the prediction function f(x), including being general, optimal, efficient, having integral solutions, and being deterministic. However, achieving all properties simultaneously is impossible for hard problems. Approaches give up certain properties, like generality, to design algorithms that satisfy the remaining desirable properties.
The document discusses probabilistic reasoning in intelligent systems using Bayesian networks. It covers the following topics:
1. Updating beliefs in a network by propagating probabilities between connected nodes using conditional probability tables.
2. Computing the posterior probability at a node given evidence elsewhere in the network by multiplying the prior at the node by the likelihood of the evidence.
3. Updating beliefs in chains, trees, and polytrees by propagating probabilities along the edges of the graph structure.
Saddlepoint approximations, likelihood asymptotics, and approximate condition...jaredtobin
Maximum likelihood methods may be inadequate for parameter estimation in models where many nuisance parameters are present. The modified profile likelihood (MPL) of Barndorff-Nielsen (1983) serves as a highly accurate approximation to the marginal or conditional likelihood, when either exist, and can be viewed as an approximate conditional likelihood when they do not. We examine the modified profile likelihood, its variants, and its connections with Laplace and saddlepoint approximations under both theoretical and pragmatic lenses.
On Foundations of Parameter Estimation for Generalized Partial Linear Models ...SSA KPI
1) The document discusses estimation methods for generalized linear models (GLMs) and generalized partial linear models (GPLMs). 2) GPLMs extend GLMs by adding a single nonparametric component to the linear predictor. 3) Parameter estimation for GPLMs is performed by maximizing a penalized likelihood function, where the penalty term controls the tradeoff between model fit and smoothness of the nonparametric component. 4) An iterative algorithm such as Newton-Raphson is used to solve the penalized maximum likelihood estimation problem.
Classifications & Misclassifications of EEG Signals using Linear and AdaBoost...IJARIIT
Epilepsy is one of the frequent brain disorder due to transient and unexpected electrical interruptions of brain. Electroencephalography (EEG) is one of the most clinically and scientifically exploited signals recorded from humans and very complex signal. EEG signals are non-stationary as it changes over time. So, discrete wavelet transform (DWT) technique is used for feature extraction. Classifications and misclassifications of EEG signals of linearly separable support vector machines are shown using training and testing datasets. Then AdaBoost support vector machine is used to get strong classifier.
This presentation provides an overview of boosting approaches for classification problems. It discusses combining classifiers through bagging and boosting to create stronger classifiers. The AdaBoost algorithm is explained in detail, including its training and classification phases. An example is provided to illustrate how AdaBoost works over multiple rounds, increasing the weights of misclassified examples to improve classification accuracy. In conclusion, AdaBoost is highlighted as an effective approach for classification problems where misclassification has severe consequences by producing highly accurate strong classifiers.
This presentation is about Multiple Classifier System (Ensemble of Classifiers). At first tell about the general idea of decision making, then address reasons and rationales of using Multiple Classifier System, after that concentrate on designing Multiple Classifier System: 1.Create an Ensemble 2.Combining Classifiers.
This document contains mathematical equations and definitions related to quantum mechanics and quantum operators. It defines operators such as momentum, position, angular momentum, and their commutation relations. It also provides equations for wave functions, energy levels, and harmonic oscillator states. Harmonic oscillator wave functions, energy eigenvalues, and operator relations are summarized.
The document discusses modeling decision making deficits in disorders that impact the frontostriatal system using computational models of reinforcement learning. It notes that many such disorders involve changes in motivation and some have genetic heritability. However, the effects of candidate genes are generally small. The author proposes using a theoretical model of reinforcement learning that incorporates data on dopamine prediction errors and the basal ganglia to help identify which genes, tasks, and measures are most relevant. The model aims to integrate findings on how dopamine affects striatal learning of positive and negative prediction errors. Data from a temporal decision making task is presented that the model can fit at both group and single subject levels. The model may help modulate reinforcement learning parameters based on neurogenetic and pharmacological
Asset Prices in Segmented and Integrated Marketsguasoni
This document summarizes a model of asset pricing in segmented and integrated markets. It begins with motivation from the financialization of commodities and market integration. It then presents a model with two regions/trees producing dividends. Equilibria are characterized for when the regions are segmented and integrated. Key results include asset prices being more cyclical and negatively correlated in segmentation, but highly positively correlated in integration. Integration always increases welfare even if it sometimes lowers asset prices and total wealth. Both regions would choose integration to access a smoother consumption stream.
This document summarizes a presentation on numerically solving spatiotemporal models from ecology by implementing an implicit finite difference method in C++. It discusses classical population dynamics models, extending these to include continuous spatial position by using reaction-diffusion systems. It describes discretizing the domain and deriving finite-difference schemes, then solving the equations using GMRES with an ILU preconditioner. Questions addressed include convergence rates and modeling plankton dynamics.
This document summarizes selection algorithms and the 1-center problem.
The selection algorithm uses a prune and search approach. It recursively partitions the dataset into subsets based on the median, pruning away elements that are guaranteed to be outside the desired rank. This results in a linear time complexity of O(n).
The 1-center problem finds the smallest circle enclosing a set of points. A constrained version restricts the center to a given line. The algorithm works by forming point pairs, computing bisectors, and recursively pruning points outside the optimal region.
By tracking the sign of distances to farthest points, the full 2D solution can also be obtained in linear time by recursively considering constrained subproblems on the x
This document describes a collapsed dynamic factor analysis model for macroeconomic forecasting. It summarizes that multivariate time series models can more accurately capture relationships between economic variables compared to univariate models. The document then presents a collapsed dynamic factor model that relates a target time series (yt) to unobserved dynamic factors (Ft) estimated from related macroeconomic data (gt). Out-of-sample forecasting experiments on US personal income and industrial production data demonstrate the model achieves more accurate point forecasts than univariate benchmarks like random walk or AR(2) models.
The document describes 17 Prolog functions for working with lists:
1. member/2 - Checks if an element is a member of a list.
2. mylength/2 - Calculates the length of a list.
3. myappend/3 - Appends two lists together.
4. replace/3 - Replaces all instances of an element with a new value in a list.
5. Various other functions for manipulating lists like reversing, inserting, deleting elements, counting occurrences, etc.
This paper models competition between multiple market makers and analyzes how increasing the number of market makers affects transaction costs for liquidity traders. It finds that:
1) There is no pure strategy equilibrium, but there exists a mixed strategy equilibrium where each market maker randomly sets prices between μ and 1.
2) Increasing the number of market makers increases transaction costs, counter to the traditional view that more competition reduces costs.
3) With elastic demand, the competitive equilibrium price rises to meet demand, but trading still occurs with positive probability as the elasticity approaches zero.
This document introduces ∞-tuples of bounded linear operators on a Banach space and conditions for an ∞-tuple to satisfy the Hypercyclicity Criterion. It defines key concepts such as hypercyclic and semi-periodic vectors. Several theorems are presented: the Hypercyclicity Criterion for ∞-Tuples provides sufficient conditions for an ∞-tuple to be hypercyclic; if an ∞-tuple satisfies these conditions and has a subset of semi-periodic vectors, then it satisfies the Hypercyclicity Criterion; and if an ∞-tuple is hypercyclic with a dense generalized kernel, then it satisfies the Hypercyclicity Criterion. The
This document describes a clustering procedure and nonparametric mixture estimation. It introduces a mixture density model where the goal is to efficiently estimate the mixture weights (αi) and component densities (fi). A two-stage clustering algorithm is proposed: 1) perform clustering on covariates (X) to estimate labels (Ik), and 2) estimate component densities (fi) using kernel density estimation within each cluster. The performance of this approach depends on the clustering method's misclassification error. A toy example with two components having disjoint support densities for X is provided to illustrate the model.
The document discusses Gauss-Seidel, Successive Over Relaxation (SOR), and block SOR methods for solving systems of linear equations. Gauss-Seidel converges faster than Jacobi iteration. SOR can further accelerate convergence by introducing a relaxation parameter ω between 0 and 2. Block SOR generalizes the approach to block-structured matrices by solving blocks simultaneously. Examples show how to apply these methods to finite difference discretizations in 2D and 3D.
This document contains a chapter on integration with 20 exercises involving calculating areas under curves. The exercises provide functions defining regions and ask the reader to calculate areas using various techniques like right endpoints, left endpoints, and trapezoid rules. The functions include polynomials, trigonometric functions, exponentials, and logarithms. Calculating areas allows practicing applying definitions of integrals to find anti-derivatives and definite integrals.
04 structured prediction and energy minimization part 1zukun
The document discusses structured prediction problems and energy minimization approaches. It describes how structured prediction involves finding the optimal prediction y* from a set of possibilities Y that maximizes an objective function g(x,y). Exactly solving such problems is difficult because Y is large but finite. The document outlines desirable properties for algorithms that evaluate the prediction function f(x), including being general, optimal, efficient, having integral solutions, and being deterministic. However, achieving all properties simultaneously is impossible for hard problems. Approaches give up certain properties, like generality, to design algorithms that satisfy the remaining desirable properties.
The document discusses probabilistic reasoning in intelligent systems using Bayesian networks. It covers the following topics:
1. Updating beliefs in a network by propagating probabilities between connected nodes using conditional probability tables.
2. Computing the posterior probability at a node given evidence elsewhere in the network by multiplying the prior at the node by the likelihood of the evidence.
3. Updating beliefs in chains, trees, and polytrees by propagating probabilities along the edges of the graph structure.
Saddlepoint approximations, likelihood asymptotics, and approximate condition...jaredtobin
Maximum likelihood methods may be inadequate for parameter estimation in models where many nuisance parameters are present. The modified profile likelihood (MPL) of Barndorff-Nielsen (1983) serves as a highly accurate approximation to the marginal or conditional likelihood, when either exist, and can be viewed as an approximate conditional likelihood when they do not. We examine the modified profile likelihood, its variants, and its connections with Laplace and saddlepoint approximations under both theoretical and pragmatic lenses.
On Foundations of Parameter Estimation for Generalized Partial Linear Models ...SSA KPI
1) The document discusses estimation methods for generalized linear models (GLMs) and generalized partial linear models (GPLMs). 2) GPLMs extend GLMs by adding a single nonparametric component to the linear predictor. 3) Parameter estimation for GPLMs is performed by maximizing a penalized likelihood function, where the penalty term controls the tradeoff between model fit and smoothness of the nonparametric component. 4) An iterative algorithm such as Newton-Raphson is used to solve the penalized maximum likelihood estimation problem.
Classifications & Misclassifications of EEG Signals using Linear and AdaBoost...IJARIIT
Epilepsy is one of the frequent brain disorder due to transient and unexpected electrical interruptions of brain. Electroencephalography (EEG) is one of the most clinically and scientifically exploited signals recorded from humans and very complex signal. EEG signals are non-stationary as it changes over time. So, discrete wavelet transform (DWT) technique is used for feature extraction. Classifications and misclassifications of EEG signals of linearly separable support vector machines are shown using training and testing datasets. Then AdaBoost support vector machine is used to get strong classifier.
This presentation provides an overview of boosting approaches for classification problems. It discusses combining classifiers through bagging and boosting to create stronger classifiers. The AdaBoost algorithm is explained in detail, including its training and classification phases. An example is provided to illustrate how AdaBoost works over multiple rounds, increasing the weights of misclassified examples to improve classification accuracy. In conclusion, AdaBoost is highlighted as an effective approach for classification problems where misclassification has severe consequences by producing highly accurate strong classifiers.
This presentation is about Multiple Classifier System (Ensemble of Classifiers). At first tell about the general idea of decision making, then address reasons and rationales of using Multiple Classifier System, after that concentrate on designing Multiple Classifier System: 1.Create an Ensemble 2.Combining Classifiers.
Kato Mivule: An Overview of Adaptive Boosting – AdaBoostKato Mivule
AdaBoost is a machine learning algorithm that uses multiple weak learners to create a strong learner. It works by assigning higher weights to misclassified examples from previous iterations and runs multiple iterations, each time adding a new weak learner that focuses on the examples with higher weights. The document presents an experiment using AdaBoost with decision stumps on a cancer dataset, finding a classification accuracy of 93.12% compared to 92.97% for decision stumps alone. ROC/AUC analysis showed AdaBoost with an AUC of 0.975 outperforming decision stumps with an AUC of 0.911, demonstrating that AdaBoost can create a more effective classifier than a single weak learner.
This document discusses machine learning and artificial intelligence. It defines machine learning as a branch of AI that allows systems to learn from data and experience. Machine learning is important because some tasks are difficult to define with rules but can be learned from examples, and relationships in large datasets can be uncovered. The document then discusses areas where machine learning is influential like statistics, brain modeling, and more. It provides an example of designing a machine learning system to play checkers. Finally, it discusses machine learning algorithm types and provides details on the AdaBoost algorithm.
2013-1 Machine Learning Lecture 06 - Artur Ferreira - A Survey on Boosting…Dongseo University
This document summarizes a survey on boosting algorithms for supervised learning. It begins with an introduction to ensembles of classifiers and boosting, describing how boosting builds ensembles by combining simple classifiers with associated contributions. The AdaBoost algorithm and its variants are then explained in detail. Experimental results on synthetic and standard datasets are presented, comparing boosting with generative and RBF weak learners. The results show that boosting algorithms can achieve low error rates, with AdaBoost performing well when weak learners are only slightly better than random.
The document discusses the AdaBoost classifier algorithm. AdaBoost is an algorithm that combines multiple weak classifiers to produce a strong classifier. It works by training weak classifiers on weighted versions of the training data and combining them through a weighted majority vote. The weights are updated at each iteration to focus on misclassified examples. The final strong classifier is a linear combination of the weak classifiers.
1. The document describes a general boosting procedure for combining weak learners to create a strong learner.
2. It involves initializing the model, learning weak learners, calculating error rates, adjusting the distribution of the training data, and combining weak learners.
3. It also describes the AdaBoost algorithm which implements this general boosting procedure and learns weak learners in sequence while focusing more on examples that previous learners got wrong.
1) The document discusses query suggestion techniques using hitting time on graphs to model relationships between queries, reformulations, and URLs.
2) It presents algorithms for calculating the hitting time between nodes in a graph and using this to determine the likelihood of queries and URLs being related.
3) Experimental results on benchmark datasets show the hitting time approach achieves good performance for query suggestion compared to other methods.
1. Position angle (θ) is measured in revolutions, degrees, or radians. Common units include 1 revolution = 360° = 2π radians.
2. Angular displacement (Δθ) is the change in position angle between an initial angle (θ1) and final angle (θ2).
3. Angular velocity (ω) is the rate of change of the angular displacement with respect to time and is measured in radians/second. Average and instantaneous angular velocity can be calculated.
This document discusses the discrete Fourier transform (DFT) and fast Fourier transform (FFT). It begins by contrasting the frequency and time domains. It then defines the DFT, showing how it samples the discrete-time Fourier transform (DTFT) at discrete frequency points. It provides an example 4-point DFT calculation. It discusses the computational complexity of the direct DFT algorithm and how the FFT reduces this to O(N log N) by decomposing the DFT into smaller transforms. It explains the decimation-in-time FFT algorithm using butterfly operations across multiple stages. Finally, it notes that the inverse FFT can be computed using the FFT along with conjugation and scaling steps.
1) The first integral evaluates to 4πi using the Cauchy integral formula applied to circles around z=1 and z=2.
2) The second integral evaluates the 4th derivative of e2z at z=-1 using a formula relating derivatives and contour integrals, giving a value of 24.
3) Both integrals are evaluated quickly using results from complex analysis without direct computation.
1. The document discusses operations that can be performed on continuous-time signals, including time reversal, time shifting, amplitude scaling, addition, multiplication, and time scaling.
2. It provides examples of each operation using the unit step function u(t) and illustrates the effect graphically. Combinations of operations are also demonstrated through examples.
3. Key operations include time shifting which delays a signal, time scaling which speeds up or slows down a signal, and their combination which first performs one operation and then the other.
1. The document discusses operations that can be performed on continuous-time signals, including time reversal, time shifting, amplitude scaling, addition, multiplication, and time scaling.
2. It provides examples of each operation using the unit step function u(t) and illustrates the effect graphically. Combinations of operations are also demonstrated through examples.
3. Key operations include time shifting which delays a signal, time scaling which speeds up or slows down a signal, and their combination which first performs one operation and then the other.
1. The document discusses various operations that can be performed on signals including time reversal, time shifting, time scaling, amplitude scaling, signal addition, and signal multiplication.
2. Examples are provided to demonstrate how to graphically represent signals and how the different operations change the signals.
3. Key steps are outlined for performing each operation including reversing the time axis, delaying or advancing signals, compressing or expanding the time axis, amplifying or attenuating signal amplitude, adding or multiplying signal values.
This document discusses uncertainty propagation techniques for determining statistics of model outputs given uncertain model inputs. It covers analytic approaches for linear models, perturbation methods for nonlinear models, and direct sampling methods. It also discusses computing moments using stochastic spectral methods like stochastic Galerkin with polynomial chaos. The document provides an example of applying perturbation and sampling methods to a nonlinear oscillator model with uncertain parameters. It compares the results from both approaches to the true natural frequency. Finally, it discusses uncertainty quantification for a HIV model and the use of prediction intervals in nuclear power plant design.
Two Dimensional Unsteady Heat Conduction in T-shaped Plate.pdfShehzaib Yousuf Khan
This document defines the geometry and boundary conditions for a transient heat transfer simulation of a T-shaped plate. It discretizes the domain into uniform elements and initializes the temperature field. It then performs explicit time stepping using the heat equation, updating temperatures at the interior nodes of each sub-domain and along their interface at each time step. The simulation runs until a stopping criteria is met, outputting temperature contour plots at each iteration.
The document discusses different types of energy including electrical, thermal, chemical, sound, electromagnetic, potential, and kinetic energy. It defines energy as the capacity to do work and discusses units of energy as joules. Power is defined as the rate at which energy is expended and is measured in watts. Examples of energy conversion efficiency are given for muscles being around 25% efficient and electric motors being around 80% efficient.
This document contains solutions to problems from Chapter 15. It provides detailed calculations and examples for various circuit analysis problems involving filters. Some key points:
- It calculates transfer functions, corner frequencies, and component values for low-pass filters, high-pass filters, and bandpass filters.
- It determines the number of poles needed in a filter to achieve a given attenuation level.
- It analyzes the transfer function of a maximally flat high-pass filter and derives the relationship between component values.
- It provides an example of designing a circuit to meet given low-frequency and high-frequency gain specifications using an op-amp.
The document demonstrates analytical techniques for analyzing and designing passive filter
This document discusses an integrate-and-dump detector used in digital communications. It describes the operation of the integrate-and-dump detector, showing how it integrates the received signal plus noise over each symbol interval. The output of the integrator is used to detect whether a 1 or 0 was transmitted. An expression is derived for the probability of detection error in terms of the signal amplitude, noise power spectral density, and symbol interval. An example is also provided to calculate the error probability for a given binary signaling scheme and system parameters.
This document contains solutions to multiple questions regarding signals and systems. Question 1 discusses periodic signals with different periods and derives a new combined periodic signal. Question 2 involves differential equations and solutions. Question 3 covers energy signals, Kirchhoff's voltage law, and solving a differential equation for the current in an RLC circuit. Question 4 finds the zero-input and zero-state responses of a linear system. Question 5 provides solutions involving Fourier series representations of periodic functions.
TD-SCDMA uses equivalent baseband signaling to represent real-valued bandpass signals as complex-valued lowpass signals, simplifying calculations. Uplink channel estimation in TD-SCDMA uses a midamble sequence and maximum likelihood estimation. A circulant matrix representation allows the channel estimation problem to be solved efficiently using fast Fourier transforms.
The document discusses several machine learning algorithms and techniques. It introduces classification, pattern recognition, clustering, association rule learning. It then covers decision trees in more detail, explaining the exact cover by 3-set problem, ID3 algorithm, CART, and C4.5 decision tree induction. Random forests are also mentioned briefly. Examples are provided to illustrate calculation of information gain and entropy measures.
Es400 fall 2012_lecuture_2_transformation_of_continuous_time_signal.pptxumavijay
This document outlines transformations that can be applied to continuous-time signals, including time reversal, time scaling, time shifting, and amplitude transformations. It also discusses properties of even and odd signals. Time reversal flips the signal across the time axis. Time scaling stretches or compresses the time axis. Time shifting slides the signal along the time axis. Amplitude transformations multiply the signal by a constant and add an offset. The product of two even signals is even, while the product of an even and odd signal is odd.
The document describes a damped mass-spring system and provides the equation of motion for analyzing the free vibration of the system. It then gives the general solution to the differential equation that describes the response x(t) in terms of the system's natural frequency, damping ratio, initial displacement, and initial velocity. The student is asked to:
1. Create a Matlab function to calculate the response x(t) for given parameter values.
2. Run sample code that plots the response for different damping ratios.
3. Calculate and submit the response at two specific cases.
This document summarizes solutions to problems involving circuit analysis using Laplace transforms.
1) The first problem analyzes a simple RC circuit and calculates the transfer function, cutoff frequency, and output response to a step input.
2) The second problem analyzes a similar RC circuit with different component values and calculates the transfer function and cutoff frequency.
3) Additional circuit examples are provided involving resistors, capacitors, and inductors. Transfer functions are derived and cutoff frequencies are calculated.
4) A multiple time constant circuit is analyzed and its frequency response is characterized.
5) Circuits involving operational amplifiers are analyzed to derive transfer functions and calculate bandwidth parameters.
The document contains references to multiple figures and tables across several pages. Figures 1, 2, 3, 4, and 5 are referenced, along with Table 1. The figures are cited in groups or individually with labels a through j.
The document discusses a lecture on next generation sequencing analysis for model and non-model organisms. It covers topics like RNA-Seq analysis, genome and RNA assembly, and introduction to the AWK programming language. The lecture also includes exercises on visualizing mapped reads, performing RNA-Seq analysis, and genome assembly. Mapping, assembly, and visualization of reads from Arabidopsis thaliana and A. lyrata are discussed.
Next generation sequencing techniques were discussed including an overview of various sequencing platforms, their output, and common analysis workflows. Mapping short reads to reference genomes using alignment programs is a key first step for most applications. Formats like FASTQ, SAM, and BAM are commonly used to store sequencing reads and mapping results.
The document summarizes two papers presented at NIPS 2010:
1) "b-Bit Minwise Hashing for Estimating Three-Way Similarities" which introduces a method called b-bit minwise hashing to estimate Jaccard similarity between three sets using only b bits per element.
2) "Functional Geometry Alignment and Localization of Brain Areas" which presents a method called functional geometry alignment to register brain images based on functional data like fMRI rather than just anatomical data. It uses diffusion maps to embed voxel activities in a low-dimensional space and aligns these functional embeddings for registration.
This document describes the Apriori algorithm for frequent itemset mining. The Apriori algorithm uses a "bottom-up" approach, where frequent subsets are extended one item at a time to generate larger itemsets. To reduce the number of candidate itemsets, the algorithm prunes any itemset whose subset is not frequent. It performs multiple passes over the transaction database and uses a hash-tree structure to count candidate itemsets efficiently.
The document describes and compares different hierarchical clustering algorithms:
1) Single-link clustering connects clusters based on the closest pair of patterns, forming elongated clusters. Complete-link connects based on the furthest pair, forming more compact clusters.
2) Complete-link is more useful than single-link for most applications as it produces more interpretable hierarchies. However, single-link can extract certain cluster types that complete-link cannot, like concentric clusters.
3) Average group linkage connects clusters based on the average distance between all pairs of patterns in the two clusters. It provides a balance between single and complete link.
1. The document discusses classification algorithms on two datasets: IRIS and USPS.
2. For IRIS, it performs k-Nearest Neighbors (k-NN) classification using 4 features to predict the class of iris flowers.
3. For USPS, it evaluates k-NN for digit recognition on images labeled 0-9, calculating distances between test and training points for varying values of k to optimize classification.
This document demonstrates using naive Bayes classification to analyze two datasets - contacts and iris data. For each dataset, the data is split into a training set and test set. A naive Bayes classifier model is generated from the training set and used to predict the classes of the test set. The predictions are then compared to the actual classes in the test set to evaluate the accuracy of the naive Bayes model. For both datasets, the naive Bayes model is able to accurately predict most of the test instances.
The document discusses analyzing a contacts dataset using R. It loads the contacts data, explores various attributes, builds a classification tree to predict "Young" status, and discusses parameter tuning. It also loads iris data, builds a classification tree to predict species using rpart with cp=0.1, plots the tree and data, and performs prediction on a test set with over 96% accuracy.
The document provides an introduction to the R programming language. It discusses how R can be downloaded and installed on various operating systems like Mac, Windows, and Linux. It demonstrates basic functions and operations in R like arithmetic, vectors, matrices, plotting, and distributions. Examples of key functions are shown including reading data, calculating statistics, importing and exporting data, and performing linear algebra operations. Resources for learning more about R programming are also listed.
The document describes the support vector machine (SVM) algorithm for classification. It discusses how SVM finds the optimal separating hyperplane between two classes by maximizing the margin between them. It introduces the concepts of support vectors, Lagrange multipliers, and kernels. The sequential minimal optimization (SMO) algorithm is also summarized, which breaks the quadratic optimization problem of SVM training into smaller subproblems to optimize two Lagrange multipliers at a time.
The document contains information about k-means clustering:
(1) It describes the basic k-means clustering algorithm which assigns data points to k clusters by minimizing the within-cluster sum of squares.
(2) It provides details on how k-means clustering is implemented, including randomly initializing cluster centers, assigning points to the closest center, and recalculating centers as the mean of each cluster.
(3) It notes some of the challenges with k-means clustering, including that it does not work well for non-convex clusters and can get stuck in local optima depending on random initialization.
The document describes hierarchical clustering algorithms. It compares the single-link and complete-link algorithms. Single-link produces elongated clusters by connecting nearby points, while complete-link produces more compact clusters by only merging groups whose furthest points are close. Complete-link generally produces more useful hierarchies but is less versatile than single-link. Average linkage is also mentioned as an alternative that calculates distances between groups as the average of all point-point distances.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
3. • 1 0
• N
• (Xi , ci )(i = 1, . . . , N ) C
XC = (No, Yes, Yes, Yes), cC = 1
4. • R:
•
•
•
1
i wi
•
N
wi = 1/N (i = 1, . . . , N )
1
• 10
wi = 1/10
1
5. • t=1,...,R
1. : t i
t
pt
i pt =
wi
i N t
i=1 wi
N
• p1 = wi = 1/10
1
t=1 t
wi =1 i
i=1
2. WeakLearner
WeakLearner ( t < 1/2 ) ht
t
N
t = pt |ht (Xi ) − ci | < 1/2
i
i=1
0, ht (Xi ) ci
ht (Xi ) − ci =
1,
Step 3
6. • t=1 WeakLearner
ID A F h1(Xi) = 1
E,F h1(Xi)=ci D,J ci=0
ID G,H,I,J h1(Xi) = 0
WeakLearner
10 2
p1 = 1/10
i
1 = 1/10 × 2 = 1/5 < 1/2
T2
WeakLearner
7. t+1
3. wi βt
t
βt = 0≤ < 1/2, 0 ≤ βt < 1
1− t
t
• β
1−|ht (Xi )−ci |
wi = wi βt
t+1 t
• εt βt
• εt βt
• WeakLearner ht
8. • t=1
1 = 0.2
1
β1 = = 0.2/0.8 = 0.25
1− 1
• A D, G J ht E, F
2
wA = wB = wC = wD = wG = wH = wI = wJ
2 2 2 2 2 2 2
= 1/10 × β1 = 0.025
1
2
wE = wF = 1/10 × β1 = 0.1
2 0
16. AdaBoost
• hf ε
= D(i)
{i|hf (Xi )=yi }
• D(i)
• R
εt t
≤ 2 t (1 − t)
t=1
• t εt<1/2
2 t (1 − t) < 1
• WeakLearner
ε
17. • 1
• R R+1
N R 1/2
R+1
wi ≥ βt
i=1 t=1
•
• N
R+1 R+1
wi ≥ wi
i=1 {i|hf (Xi )=yi }
t 1−|hf (Xi )−yi |
t+1
wi = wi βi
R
1−|hf (Xi )−yi |
t+1
wi = D(i) βt
{i|hf (Xi )=yi } {i|hf (Xi )=yi } t=1
18. R hf (hf (Xi ) = yi )
1−|hf (Xi )−yi |
βt hf (Xi ) = 1 yi = 0 hf (Xi ) = 0
t=1
2
hf 2
hf (Xi ) = 1 yi = 0 5.1
hf (Xi ) = 1 yi = 0, hf(Xi)=1
(hf (Xi ) = R i )
y R
1
Xi ) = 1 yi = 0 h(− log βt )hf (Xi ) y≥ = 1 (− log βt )
f (Xi ) = 0 i
t=1 t=1
2
R
0 t=1 (log5.1
βt )
R R R
1 1
− log βt )hf (Xi ) ≥ (− log(log βt )(1 − hf (Xi )) ≥
βt ) (log βt )
2
t=1 t=1 2 t=1
1 − hf (Xi ) = 1− | hf (Xi ) − yi |
R R 1/2
R
1t f (Xi )−yi | ≥
1−|h
g βt )(1 − hf (Xi )) ≥ (log βt ) β βt
t=1 2 t=1
t=1
19. t t
t=1 t=1
hf (Xi )hf (Xi ) = 0 yi = i1= 1
=0 y 5.1
R R
1
(− log βt )ht (Xi ) < (− log βt )
t=1 t=1
2
174 −1 hf (Xi ) = 1− | ht (Xi ) 5 yi |
−
1
R R 2
1−|ht (Xi )−yi |
βt > βt
t=1 t=1
hf (Xi ) = 1 yi = 0 hf (Xi ) =
yi = 1
1
R R 2
1−|ht (Xi )−yi |
βt ≥ βt
t=1 t=1
21. = ·
t=1 βt
t=1
• 2
5.2 • 5.2 N N
t+1
wi N ≥ t
wi N× 2 i
i=1
t+1
wi i=1≥ wi × 2
t
i
•
: α≥0 r = {0, 1}
i=1 i=1
: α≥0 r = {0, 1}
αr ≤ 1 − (1 − α)r
αr ≤ 1 − (1 − α)r
22. 5.6. 175
N N
1−|ht (Xi )−yi |
t+1
wi = t
wi βt
i=1 i=1
N
≤ wi (1 − (1 − βt )(1 − |ht (Xi ) − yi |))
t
i=1
N N N
= wi − (1 − βt )
t t
wi − wi |ht (Xi ) − yi |
t
i=1 i=1 i=1
N N N
= wi − (1 − βt )
t t
wi − t
t
wi
i=1 i=1 i=1
N N
= wi − (1 − βt )
t t
wi (1 − t )
i=1 i=1
N
= t
wi × (1 − (1 − βt )(1 − t ))
i=1
βt = t /(1 − t)
N
= t
wi ×2 t
i=1
23. •
5.3 t WeakLearner
•
t
εt t WeakLearner
hf hf ε
R
≤ 2 t (1 − t)
• 1/2
t=1
R N N N R
: 5.1 βt ≤ 5.2 wi
R+1
≤ R
wi ×2 t ≤ 1
wi 2 t
t=1 t=1
R 1/2 i=1 N i=1 i=1
N
βt wi = 1
1
≤ R+1
wi ( 5.1 )
t=1 i=1
i=1
R
N
= 2
≤
t=1
t R
wi × 2 t( 5.2 )
i=1
βt = t /(1 − t ) 5.2 t = R − 1, R − 2, . . . , 1
R R
−1/2 N R
≤ 2 t× βt = 12 t (1 − t)
≤ wi 2 t
t=1 t=1