Nonparametric Density Estimation under Distribution Drift
This work addresses the challenge of adapting density estimation to non-stationary environments, which is incremental as it generalizes prior results on agnostic learning under drift.
The paper tackles the problem of nonparametric density estimation when the underlying distribution changes over time, establishing tight minimax risk bounds for both discrete and continuous smooth densities under various drift models.
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.