# Nonparametric Density Estimation under Distribution Drift

arXiv: https://arxiv.org/abs/2302.02460 · HTML: https://mlsanity.com/paper/2302.02460/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 5 Feb 2023.

## Builds on (most cited first, 5 of 5)

- [Online Forecasting of Total-Variation-bounded Sequences](https://mlsanity.com/paper/1906.03364/) (2019)
- [Batch Stationary Distribution Estimation](https://mlsanity.com/paper/2003.00722/) (2020)
- [Statistical Learning under Nonstationary Mixing Processes](https://mlsanity.com/paper/1512.08064/) (2015)
- [Adaptive Online Estimation of Piecewise Polynomial Trends](https://mlsanity.com/paper/2010.00073/) (2020)
- [Learning with a Drifting Target Concept](https://mlsanity.com/paper/1505.05215/) (2015)

## Built on by (most cited first, 6 of 6)

- [An Adaptive Algorithm for Learning with Unknown Distribution Drift](https://mlsanity.com/paper/2305.02252/) (2023)
- [Sparse Prefix Caching for Hybrid and Recurrent LLM Serving](https://mlsanity.com/paper/2605.05219/) (2026)
- [An Improved Algorithm for Learning Drifting Discrete Distributions](https://mlsanity.com/paper/2403.05446/) (2024)
- [An Adaptive Method for Weak Supervision with Drifting Data](https://mlsanity.com/paper/2306.01658/) (2023)
- [Dynamic estimation of slowly varying sequences](https://mlsanity.com/paper/2606.23655/) (2026)
- [Beyond Aggregate Drift: Optimal Client-Specific Windows in Federated Learning](https://mlsanity.com/paper/2610.15543/) (2026)

## Abstract (arXiv)

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.