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E-raamat: Machine Learning in Non–Stationary Environments – Introduction to Covariate Shift Adaptation: Introduction to Covariate Shift Adaptation

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(Tokyo Institute of Technology), (ATR Brain Information Communication Research Laboratory Group)
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Machine Learning in Non–Stationary Environments – Introduction to Covariate Shift Adaptation: Introduction to Covariate Shift AdaptationSuurem pilt
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As the power of computing has grown over the past few decades, the field of machinelearning has advanced rapidly in both theory and practice. Machine learning methods are usuallybased on the assumption that the data generation mechanism does not change over time. Yet real-worldapplications of machine learning, including image recognition, natural language processing, speechrecognition, robot control, and bioinformatics, often violate this common assumption. Dealing withnon-stationarity is one of modern machine learning's greatest challenges. This book focuses on aspecific non-stationary environment known as covariate shift, in which the distributions of inputs(queries) change but the conditional distribution of outputs (answers) is unchanged, and presentsmachine learning theory, algorithms, and applications to overcome this variety of non-stationarity.After reviewing the state-of-the-art research in the field, the authors discuss topics that includelearning under covariate shift, model selection, importance estimation, and active learning. Theydescribe such real world applications of covariate shift adaption as brain-computer interface,speaker identification, and age prediction from facial images. With this book, they aim to encouragefuture research in machine learning, statistics, and engineering that strives to create trulyautonomous learning machines able to learn under non-stationarity.

Foreword xi
Preface xiii
I Introduction
1 Introduction and Problem Formulation
3(18)
1.1 Machine Learning under Covariate Shift
3(2)
1.2 Quick Tour of Covariate Shift Adaptation
5(2)
1.3 Problem Formulation
7(7)
1.3.1 Function Learning from Examples
7(1)
1.3.2 Loss Functions
8(1)
1.3.3 Generalization Error
9(1)
1.3.4 Covariate Shift
9(1)
1.3.5 Models for Function Learning
10(3)
1.3.6 Specification of Models
13(1)
1.4 Structure of This Book
14(7)
1.4.1 Part II: Learning under Covariate Shift
14(3)
1.4.2 Part III: Learning Causing Covariate Shift
17(4)
II Learning Under Covariate Shift
2 Function Approximation
21(26)
2.1 Importance-Weighting Techniques for Covariate Shift Adaptation
22(3)
2.1.1 Importance-Weighted ERM
22(1)
2.1.2 Adaptive IWERM
23(1)
2.1.3 Regularized IWERM
23(2)
2.2 Examples of Importance-Weighted Regression Methods
25(10)
2.2.1 Squared Loss: Least-Squares Regression
26(4)
2.2.2 Absolute Loss: Least-Absolute Regression
30(1)
2.2.3 Huber Loss: Huber Regression
31(2)
2.2.4 Deadzone-Linear Loss: Support Vector Regression
33(2)
2.3 Examples of Importance-Weighted Classification Methods
35(5)
2.3.1 Squared Loss: Fisher Discriminant Analysis
36(2)
2.3.2 Logistic Loss: Logistic Regression Classifier
38(1)
2.3.3 Hinge Loss: Support Vector Machine
39(1)
2.3.4 Exponential Loss: Boosting
40(1)
2.4 Numerical Examples
40(5)
2.4.1 Regression
40(1)
2.4.2 Classification
41(4)
2.5 Summary and Discussion
45(2)
3 Model Selection
47(26)
3.1 Importance-Weighted Akaike Information Criterion
47(3)
3.2 Importance-Weighted Subspace Information Criterion
50(14)
3.2.1 Input Dependence vs. Input Independence in Generalization Error Analysis
51(2)
3.2.2 Approximately Correct Models
53(1)
3.2.3 Input-Dependent Analysis of Generalization Error
54(10)
3.3 Importance-Weighted Cross-Validation
64(2)
3.4 Numerical Examples
66(4)
3.4.1 Regression
66(3)
3.4.2 Classification
69(1)
3.5 Summary and Discussion
70(3)
4 Importance Estimation
73(30)
4.1 Kernel Density Estimation
73(2)
4.2 Kernel Mean Matching
75(1)
4.3 Logistic Regression
76(2)
4.4 Kullback-Leibler Importance Estimation Procedure
78(5)
4.4.1 Algorithm
78(3)
4.4.2 Model Selection by Cross-Validation
81(1)
4.4.3 Basis Function Design
82(1)
4.5 Least-Squares Importance Fitting
83(4)
4.5.1 Algorithm
83(1)
4.5.2 Basis Function Design and Model Selection
84(1)
4.5.3 Regularization Path Tracking
85(2)
4.6 Unconstrained Least-Squares Importance Fitting
87(1)
4.6.1 Algorithm
87(1)
4.6.2 Analytic Computation of Leave-One-Out Cross-Validation
88(1)
4.7 Numerical Examples
88(6)
4.7.1 Setting
90(1)
4.7.2 Importance Estimation by KLIEP
90(2)
4.7.3 Covariate Shift Adaptation by IWLS and IWCV
92(2)
4.8 Experimental Comparison
94(7)
4.9 Summary
101(2)
5 Direct Density-Ratio Estimation with Dimensionality Reduction
103(22)
5.1 Density Difference in Hetero-Distributional Subspace
103(1)
5.2 Characterization of Hetero-Distributional Subspace
104(2)
5.3 Identifying Hetero-Distributional Subspace
106(6)
5.3.1 Basic Idea
106(2)
5.3.2 Fisher Discriminant Analysis
108(1)
5.3.3 Local Fisher Discriminant Analysis
109(3)
5.4 Using LFDA for Finding Hetero-Distributional Subspace
112(1)
5.5 Density-Ratio Estimation in the Hetero-Distributional Subspace
113(1)
5.6 Numerical Examples
113(8)
5.6.1 Illustrative Example
113(4)
5.6.2 Performance Comparison Using Artificial Data Sets
117(4)
5.7 Summary
121(4)
6 Relation to Sample Selection Bias
125(12)
6.1 Heckman's Sample Selection Model
125(4)
6.2 Distributional Change and Sample Selection Bias
129(2)
6.3 The Two-Step Algorithm
131(3)
6.4 Relation to Covariate Shift Approach
134(3)
7 Applications of Covariate Shift Adaptation
137(46)
7.1 Brain-Computer Interface
137(5)
7.1.1 Background
137(1)
7.1.2 Experimental Setup
138(2)
7.1.3 Experimental Results
140(2)
7.2 Speaker identification
142(7)
7.2.1 Background
142(1)
7.2.2 Formulation
142(2)
7.2.3 Experimental Results
144(5)
7.3 Natural Language Processing
149(3)
7.3.1 Formulation
149(2)
7.3.2 Experimental Results
151(1)
7.4 Perceived Age Prediction from Face Images
152(5)
7.4.1 Background
152(1)
7.4.2 Formulation
153(1)
7.4.3 Incorporating Characteristics of Human Age Perception
153(2)
7.4.4 Experimental Results
155(2)
7.5 Human Activity Recognition from Accelerometric Data
157(8)
7.5.1 Background
157(1)
7.5.2 Importance-Weighted Least-Squares Probabilistic Classifier
157(3)
7.5.3 Experimental Results
160(5)
7.6 Sample Reuse in Reinforcement Learning
165(18)
7.6.1 Markov Decision Problems
165(1)
7.6.2 Policy Iteration
166(1)
7.6.3 Value Function Approximation
167(1)
7.6.4 Sample Reuse by Covariate Shift Adaptation
168(1)
7.6.5 On-Policy vs. Off-Policy
169(1)
7.6.6 Importance Weighting in Value Function Approximation
170(4)
7.6.7 Automatic Selection of the Flattening Parameter
174(1)
7.6.8 Sample Reuse Policy Iteration
175(1)
7.6.9 Robot Control Experiments
176(7)
III Learning Causing Covariate Shift
8 Active Learning
183(32)
8.1 Preliminaries
183(5)
8.1.1 Setup
183(2)
8.1.2 Decomposition of Generalization Error
185(3)
8.1.3 Basic Strategy of Active Learning
188(1)
8.2 Population-Based Active Learning Methods
188(10)
8.2.1 Classical Method of Active Learning for Correct Models
189(1)
8.2.2 Limitations of Classical Approach and Countermeasures
190(1)
8.2.3 Input-Independent Variance-Only Method
191(2)
8.2.4 Input-Dependent Variance-Only Method
193(2)
8.2.5 Input-Independent Bias-and-Variance Approach
195(3)
8.3 Numerical Examples of Population-Based Active Learning Methods
198(6)
8.3.1 Setup
198(2)
8.3.2 Accuracy of Generalization Error Estimation
200(2)
8.3.3 Obtained Generalization Error
202(2)
8.4 Pool-Based Active Learning Methods
204(5)
8.4.1 Classical Active Learning Method for Correct Models and Its Limitations
204(1)
8.4.2 Input-Independent Variance-Only Method
205(1)
8.4.3 Input-Dependent Variance-Only Method
206(1)
8.4.4 Input-Independent Bias-and-Variance Approach
207(2)
8.5 Numerical Examples of Pool-Based Active Learning Methods
209(3)
8.6 Summary and Discussion
212(3)
9 Active Learning with Model Selection
215(10)
9.1 Direct Approach and the Active Learning/Model Selection Dilemma
215(1)
9.2 Sequential Approach
216(2)
9.3 Batch Approach
218(1)
9.4 Ensemble Active Learning
219(1)
9.5 Numerical Examples
220(3)
9.5.1 Setting
220(1)
9.5.2 Analysis of Batch Approach
221(1)
9.5.3 Analysis of Sequential Approach
222(1)
9.5.4 Comparison of Obtained Generalization Error
222(1)
9.6 Summary and Discussion
223(2)
10 Applications of Active Learning
225(16)
10.1 Design of Efficient Exploration Strategies in Reinforcement Learning
225(9)
10.1.1 Efficient Exploration with Active Learning
225(1)
10.1.2 Reinforcement Learning Revisited
226(2)
10.1.3 Decomposition of Generalization Error
228(1)
10.1.4 Estimating Generalization Error for Active Learning
229(1)
10.1.5 Designing Sampling Policies
230(1)
10.1.6 Active Learning in Policy Iteration
231(1)
10.1.7 Robot Control Experiments
232(2)
10.2 Wafer Alignment in Semiconductor Exposure Apparatus
234(7)
IV Conclusions
11 Conclusions and Future Prospects
241(2)
11.1 Conclusions
241(1)
11.2 Future Prospects
242(1)
Appendix: List of Symbols and Abbreviations 243(4)
Bibliography 247(12)
Index 259
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