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Faster Rates via Active Learning
Published on Feb 4, 20253747 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