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Density Ratio Estimation in Machine Learning
Published on Dec 03, 20125922 Views
In statistical machine learning, avoiding density estimation is essential because it is often more difficult than solving a target machine learning problem itself. This is often referred to as Vapnik
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Chapter list
Density Ratio Estimation in Machine Learning00:00
Machine Learning (ML)00:47
Universal Approach01:15
Task-Specific Approach02:25
Task-Specific Approach (cont.)03:19
Intermediate Approach04:09
Density-Ratio Estimation05:22
Intuitive Justification06:29
Quick Conclusions08:16
Organization of This Lecture09:15
Density Ratio Estimation: Problem Formulation10:08
Density Estimation Approach10:41
Density Fitting11:52
Kullback-Leibler Importance Estimation Procedure (KLIEP)11:59
KLIEP: Formulation13:19
KLIEP: Algorithm14:55
KLIEP: Convergence Properties16:04
KLIEP: Numerical Example18:37
KLIEP: Summary20:25
Density-Ratio Fitting23:10
Least-Squares Importance Fitting (LSIF)23:26
Constrained LSIF Formulation25:00
cLSIF: Regularization Path Tracking26:11
Unconstrained LSIF Formulation28:56
uLSIF: Analytic LOOCV Score30:15
uLSIF: Theoretical Properties31:17
uLSIF: Numerical Example32:32
LSIF: Summary34:36
Importance sampling38:00
Learning under Covariate Shift38:43
Ordinary Least-Squares (OLS)40:34
Law of Large Numbers41:44
Importance Weighting42:42
Importance-Weighted Least-Squares43:50
Model Selection (1)44:45
Model Selection (2)46:39
Experiments: Speaker Identification48:01
Experiments: Text Segmentation49:57
Other Applications52:10
Distribution comparison55:38
Inlier-Based Outlier Detection55:56
Experiments59:47
Failure Prediction in Hard-Disk Drives01:00:49
Other Applications01:02:50
Divergence Estimation01:03:41
Real-World Applications01:04:16
Mutual Information Estimation (1)01:07:04
Mutual Information Estimation (2)01:07:29
Experiments: Methods Compared01:09:11
Datasets for Evaluation01:09:24
MI Approximation Error01:09:58
Estimation of Squared-Loss Mutual Information (SMI)01:11:19
Usage of SMI Estimator01:12:30
Sufficient Dimension Reduction01:15:56
Sufficient Dimension Reduction via SMI Maximization01:17:37
Experiments01:18:03
Conditional probability estimation01:20:12
Conditional Density Estimation01:23:40
Experiments: Transition Estimation for Mobile Robot01:25:48
Probabilistic Classification01:28:00
Numerical Example01:30:23
More Experiments01:31:12
Other Applications01:31:39
More on Density Ratio Estimation01:32:41
Direct Density-Ratio Estimation with Dimensionality Reduction (D3)01:33:04
Hetero-distributional Subspace (HS)01:33:28
Conclusions01:35:12
Books on Density Ratios01:36:17
Acknowledgements01:36:34