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Faster Rates via Active Learning
Published on 2007-02-253747 Views
Traditional sampling and statistical learning theories deal with data collection processes that are completely independent of the target function to be estimated, aside from possible a priori specific
Presentation
Faster Rates via Active Learning00:02
Laser Scanning of a Landscape or Object05:29
slide306:22
slide407:18
“What” vs. “Where” Information08:09
Passive vs. Active Learning10:14
Active Learning10:58
Notation12:47
Selective Sensing13:11
Adaptive Sampling15:52
Basic Problem – Passive Learning16:00
Basic Problem – Active Learning16:31
Main Results17:05
Passive Learning in One Dimension18:37
Active Learning in One Dimension18:52
Passive Learning in Noiseless Conditions19:57
Active Learning in Noiseless Conditions20:17
Passive Learning in Noise20:55
Active Learning in Noise21:24
A Probabilistic Bisection22:01
Adaptive Sampling via Bayesian Bisection24:59
slide2626:44
Multidimensional Nonparametric Problems28:46
Passive Learning via Recursive Dyadic Partitions30:50
Piecewise Constant Error Analysis32:06
Passive Learning in Action32:51
Can Active Learning Do Better ? Boundary Fragments33:25
Active Learning of Boundary Fragments34:11
Minimax Lower Bounds for Active Learning35:35
Active Learning of Smoother Boundaries36:12
Limitations of Boundary Fragment Model37:50
Active Learning of General Boundaries38:27
Basic Approach: Intuition39:54
Example: Piecewise Smooth Function41:22
Sketch of Proof of Main Theorem42:12
Sketch of Proof: Stage 144:06
Sketch of Proof: Stage 246:13
Sketch of Proof: Overall error bound47:52
Controlling the Bias48:57
Multi-Stage Adaptive Sampling 49:49
Conclusions50:56
Spatial Adaptivity and Active Learning51:11