- grunewalder18
Accepted author manuscript, 248 KB, PDF document

- http://proceedings.mlr.press/v84/grunewalder18a.html
Final published version

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

Published

**Plug-in Estimators for Conditional Expectations and Probabilities.** / Grunewalder, Steffen.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

Grunewalder, S 2018, Plug-in Estimators for Conditional Expectations and Probabilities. in A Storkey & F Perez-Cruz (eds), *Proceedings of the 21st International Conference on Artificial Intelligence and Statistics.* Proceedings of Machine Learning Research, vol. 84, PMLR, pp. 1513-1521, 21st International Conference on Artificial Intelligence and Statistics , Lanzarote, Spain., Playa Blanca, Lanzarote, Spain, 9/04/18. <http://proceedings.mlr.press/v84/grunewalder18a.html>

Grunewalder, S. (2018). Plug-in Estimators for Conditional Expectations and Probabilities. In A. Storkey, & F. Perez-Cruz (Eds.), *Proceedings of the 21st International Conference on Artificial Intelligence and Statistics *(pp. 1513-1521). (Proceedings of Machine Learning Research; Vol. 84). PMLR. http://proceedings.mlr.press/v84/grunewalder18a.html

Grunewalder S. Plug-in Estimators for Conditional Expectations and Probabilities. In Storkey A, Perez-Cruz F, editors, Proceedings of the 21st International Conference on Artificial Intelligence and Statistics. PMLR. 2018. p. 1513-1521. (Proceedings of Machine Learning Research).

@inproceedings{31cb02563263448091dd627c9d31487d,

title = "Plug-in Estimators for Conditional Expectations and Probabilities",

abstract = "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 {\OE}0; 1=2/ controls a lower bound on the size of sets wecan estimate given n samples. We gain similar results for Kolmogorov{\textquoteright}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",

author = "Steffen Grunewalder",

note = "Proceedings of the 21st International Conference on Artificial Intelligence and Statistics (AISTATS) 2018, Lanzarote, Spain. PMLR: Volume 84. Copyright 2018 by the author(s).; 21st International Conference on Artificial Intelligence and Statistics , Lanzarote, Spain., AISTATS 2018 ; Conference date: 09-04-2018 Through 11-04-2018",

year = "2018",

month = apr,

day = "1",

language = "English",

series = "Proceedings of Machine Learning Research",

publisher = "PMLR",

pages = "1513--1521",

editor = "Amos Storkey and Fernando Perez-Cruz",

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url = "https://www.aistats.org/",

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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

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