Statistical Learning under Nonstationary Mixing Processes

Steve Hanneke, Liu Yang
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:1678-1686, 2019.

Abstract

We study a special case of the problem of statistical learning without the i.i.d. assumption. Specifically, we suppose a learning method is presented with a sequence of data points, and required to make a prediction (e.g., a classification) for each one, and can then observe the loss incurred by this prediction. We go beyond traditional analyses, which have focused on stationary mixing processes or nonstationary product processes, by combining these two relaxations to allow nonstationary mixing processes. We are particularly interested in the case of $\beta$-mixing processes, with the sum of changes in marginal distributions growing sublinearly in the number of samples. Under these conditions, we propose a learning method, and establish that for bounded VC subgraph classes, the cumulative excess risk grows sublinearly in the number of predictions, at a quantified rate.

Cite this Paper


BibTeX
@InProceedings{pmlr-v89-hanneke19a, title = {Statistical Learning under Nonstationary Mixing Processes}, author = {Hanneke, Steve and Yang, Liu}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {1678--1686}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/hanneke19a/hanneke19a.pdf}, url = {http://proceedings.mlr.press/v89/hanneke19a.html}, abstract = {We study a special case of the problem of statistical learning without the i.i.d. assumption. Specifically, we suppose a learning method is presented with a sequence of data points, and required to make a prediction (e.g., a classification) for each one, and can then observe the loss incurred by this prediction. We go beyond traditional analyses, which have focused on stationary mixing processes or nonstationary product processes, by combining these two relaxations to allow nonstationary mixing processes. We are particularly interested in the case of $\beta$-mixing processes, with the sum of changes in marginal distributions growing sublinearly in the number of samples. Under these conditions, we propose a learning method, and establish that for bounded VC subgraph classes, the cumulative excess risk grows sublinearly in the number of predictions, at a quantified rate.} }
Endnote
%0 Conference Paper %T Statistical Learning under Nonstationary Mixing Processes %A Steve Hanneke %A Liu Yang %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-hanneke19a %I PMLR %P 1678--1686 %U http://proceedings.mlr.press/v89/hanneke19a.html %V 89 %X We study a special case of the problem of statistical learning without the i.i.d. assumption. Specifically, we suppose a learning method is presented with a sequence of data points, and required to make a prediction (e.g., a classification) for each one, and can then observe the loss incurred by this prediction. We go beyond traditional analyses, which have focused on stationary mixing processes or nonstationary product processes, by combining these two relaxations to allow nonstationary mixing processes. We are particularly interested in the case of $\beta$-mixing processes, with the sum of changes in marginal distributions growing sublinearly in the number of samples. Under these conditions, we propose a learning method, and establish that for bounded VC subgraph classes, the cumulative excess risk grows sublinearly in the number of predictions, at a quantified rate.
APA
Hanneke, S. & Yang, L.. (2019). Statistical Learning under Nonstationary Mixing Processes. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:1678-1686 Available from http://proceedings.mlr.press/v89/hanneke19a.html.

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