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Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review
Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review
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TY - GEN
T1 - Plug-in Estimators for Conditional Expectations and Probabilities
AU - Grunewalder, Steffen
N1 - Proceedings of the 21st International Conference on Artificial Intelligence and Statistics (AISTATS) 2018, Lanzarote, Spain. PMLR: Volume 84. Copyright 2018 by the author(s).
PY - 2018/4/1
Y1 - 2018/4/1
N2 - We study plug-in estimators of conditional expectations and probabilities, and we provide asystematic analysis of their rates of convergence. The plug-in approach is particularly useful inthis setting since it introduces a natural link to VC- and empirical process theory. We make useof this link to derive rates of convergence that hold uniformly over large classes of functionsand sets, and under various conditions. For instance, we demonstrate that elementary conditionalprobabilities are estimated by these plug-in estimators with a rate of n˛1=2 if one conditionswith a VC-class of sets and where ˛ 2 Œ0; 1=2/ controls a lower bound on the size of sets wecan estimate given n samples. We gain similar results for Kolmogorov’s conditional expectationand probability which generalize the elementary forms of conditioning. Due to their simplicity,plug-in estimators can be evaluated in linear time and there is no up-front cost for inference
AB - We study plug-in estimators of conditional expectations and probabilities, and we provide asystematic analysis of their rates of convergence. The plug-in approach is particularly useful inthis setting since it introduces a natural link to VC- and empirical process theory. We make useof this link to derive rates of convergence that hold uniformly over large classes of functionsand sets, and under various conditions. For instance, we demonstrate that elementary conditionalprobabilities are estimated by these plug-in estimators with a rate of n˛1=2 if one conditionswith a VC-class of sets and where ˛ 2 Œ0; 1=2/ controls a lower bound on the size of sets wecan estimate given n samples. We gain similar results for Kolmogorov’s conditional expectationand probability which generalize the elementary forms of conditioning. Due to their simplicity,plug-in estimators can be evaluated in linear time and there is no up-front cost for inference
M3 - Conference contribution/Paper
T3 - Proceedings of Machine Learning Research
SP - 1513
EP - 1521
BT - Proceedings of the 21st International Conference on Artificial Intelligence and Statistics
A2 - Storkey, Amos
A2 - Perez-Cruz, Fernando
PB - PMLR
T2 - 21st International Conference on Artificial Intelligence and Statistics , Lanzarote, Spain.
Y2 - 9 April 2018 through 11 April 2018
ER -