Generalization bounds for minimum volume set estimation based on Markovian data

Patrice Bertail; Gabriela Ciołek; Stephan Clémençon

Generalization bounds for minimum volume set estimation based on Markovian data

Patrice Bertail, Gabriela Ciołek, Stephan Clémençon

Research output: Contribution to conference › Paper › peer-review

Abstract

The main goal of this paper is to establish generalization bounds for minimum volume set estimation for regenerative Markov chains. We obtain new maximal concentration inequality in order to show that learning rate bounds depend not only on the complexity of the class of candidate sets but also on the ergodicity rate of the chain X, expressed in terms of tail conditions for the length of the regenerative cycles. Finally, we show that it is straightforward to extend the preceding results to the Harris recurrent case.

Original language	English
Publication status	Published - 1 Jan 2018
Externally published	Yes
Event	2018 International Symposium on Artificial Intelligence and Mathematics, ISAIM 2018 - Fort Lauderdale, United States Duration: 3 Jan 2018 → 5 Jan 2018

Conference

Conference	2018 International Symposium on Artificial Intelligence and Mathematics, ISAIM 2018
Country/Territory	United States
City	Fort Lauderdale
Period	3/01/18 → 5/01/18

Cite this

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title = "Generalization bounds for minimum volume set estimation based on Markovian data",

abstract = "The main goal of this paper is to establish generalization bounds for minimum volume set estimation for regenerative Markov chains. We obtain new maximal concentration inequality in order to show that learning rate bounds depend not only on the complexity of the class of candidate sets but also on the ergodicity rate of the chain X, expressed in terms of tail conditions for the length of the regenerative cycles. Finally, we show that it is straightforward to extend the preceding results to the Harris recurrent case.",

author = "Patrice Bertail and Gabriela Cio{\l}ek and Stephan Cl{\'e}men{\c c}on",

note = "Publisher Copyright: {\textcopyright} 2018 University of Virginia. All rights reserved.; 2018 International Symposium on Artificial Intelligence and Mathematics, ISAIM 2018 ; Conference date: 03-01-2018 Through 05-01-2018",

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AU - Ciołek, Gabriela

AU - Clémençon, Stephan

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N2 - The main goal of this paper is to establish generalization bounds for minimum volume set estimation for regenerative Markov chains. We obtain new maximal concentration inequality in order to show that learning rate bounds depend not only on the complexity of the class of candidate sets but also on the ergodicity rate of the chain X, expressed in terms of tail conditions for the length of the regenerative cycles. Finally, we show that it is straightforward to extend the preceding results to the Harris recurrent case.

AB - The main goal of this paper is to establish generalization bounds for minimum volume set estimation for regenerative Markov chains. We obtain new maximal concentration inequality in order to show that learning rate bounds depend not only on the complexity of the class of candidate sets but also on the ergodicity rate of the chain X, expressed in terms of tail conditions for the length of the regenerative cycles. Finally, we show that it is straightforward to extend the preceding results to the Harris recurrent case.

M3 - Paper

AN - SCOPUS:85069647984

T2 - 2018 International Symposium on Artificial Intelligence and Mathematics, ISAIM 2018

Y2 - 3 January 2018 through 5 January 2018

ER -

Generalization bounds for minimum volume set estimation based on Markovian data

Abstract

Conference

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