An Improved Algorithm for Learning Drifting Discrete Distributions

TL;DR

This paper introduces an adaptive algorithm for estimating changing discrete distributions over time, balancing statistical and drift errors without prior knowledge of the drift, and applicable to distributions with infinite support.

Contribution

The paper presents a novel adaptive algorithm that dynamically balances estimation errors in drifting distributions without prior drift knowledge, extending to infinite support cases.

Findings

The algorithm effectively balances bias and variance in distribution estimation.

It provides data-dependent bounds for statistical error.

It handles distributions with infinite support.

Abstract

We present a new adaptive algorithm for learning discrete distributions under distribution drift. In this setting, we observe a sequence of independent samples from a discrete distribution that is changing over time, and the goal is to estimate the current distribution. Since we have access to only a single sample for each time step, a good estimation requires a careful choice of the number of past samples to use. To use more samples, we must resort to samples further in the past, and we incur a drift error due to the bias introduced by the change in distribution. On the other hand, if we use a small number of past samples, we incur a large statistical error as the estimation has a high variance. We present a novel adaptive algorithm that can solve this trade-off without any prior knowledge of the drift. Unlike previous adaptive results, our algorithm characterizes the statistical error using data-dependent bounds. This technicality enables us to overcome the limitations of the previous work that require a fixed finite support whose size is known in advance and that cannot change over time. Additionally, we can obtain tighter bounds depending on the complexity of the drifting distribution, and also consider distributions with infinite support.