Nonparametric Density Estimation under Distribution Drift

Alessio Mazzetto, Eli Upfal
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:24251-24270, 2023.

Abstract

We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current distribution. We prove tight minimax risk bounds for both discrete and continuous smooth densities, where the minimum is over all possible estimates and the maximum is over all possible distributions that satisfy the drift constraints. Our technique handles a broad class of drift models and generalizes previous results on agnostic learning under drift.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-mazzetto23a, title = {Nonparametric Density Estimation under Distribution Drift}, author = {Mazzetto, Alessio and Upfal, Eli}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {24251--24270}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/mazzetto23a/mazzetto23a.pdf}, url = {https://proceedings.mlr.press/v202/mazzetto23a.html}, abstract = {We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current distribution. We prove tight minimax risk bounds for both discrete and continuous smooth densities, where the minimum is over all possible estimates and the maximum is over all possible distributions that satisfy the drift constraints. Our technique handles a broad class of drift models and generalizes previous results on agnostic learning under drift.} }
Endnote
%0 Conference Paper %T Nonparametric Density Estimation under Distribution Drift %A Alessio Mazzetto %A Eli Upfal %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-mazzetto23a %I PMLR %P 24251--24270 %U https://proceedings.mlr.press/v202/mazzetto23a.html %V 202 %X We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current distribution. We prove tight minimax risk bounds for both discrete and continuous smooth densities, where the minimum is over all possible estimates and the maximum is over all possible distributions that satisfy the drift constraints. Our technique handles a broad class of drift models and generalizes previous results on agnostic learning under drift.
APA
Mazzetto, A. & Upfal, E.. (2023). Nonparametric Density Estimation under Distribution Drift. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:24251-24270 Available from https://proceedings.mlr.press/v202/mazzetto23a.html.

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