Nonparametric Density Estimation under Distribution Drift

TL;DR

This paper develops minimax risk bounds for nonparametric density estimation in non-stationary environments where the underlying distribution drifts over time, extending previous models to broader drift scenarios.

Contribution

It introduces tight minimax risk bounds for density estimation under various drift models, generalizing prior results in agnostic learning with distribution drift.

Findings

Established tight minimax risk bounds for discrete and continuous densities.

Generalized techniques to handle a broad class of drift models.

Extended theoretical understanding of density estimation under non-stationarity.

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.