Quasi-Bayes empirical Bayes: a sequential approach to the Poisson compound decision problem

2024-11-12

AI Summary

This paper addresses the problem of sequential estimation of the Poisson mean under streaming data. We propose a novel quasi-Bayesian sequential method that departs from conventional empirical Bayes approaches designed for static settings. To our knowledge, this is the first work to introduce Newton-type quasi-Bayesian iteration into online Poisson compound decision problems, achieving per-step computational complexity of O(1) and an asymptotically optimal regret bound of O(log T). The method integrates quasi-Bayesian inference with the empirical Bayes framework, ensuring frequentist consistency of parameter estimates while substantially outperforming state-of-the-art batch algorithms. Extensive experiments on both synthetic and real-world datasets validate its superior estimation accuracy, real-time responsiveness, and computational efficiency. Our approach establishes a new paradigm for online statistical inference on streaming count data—uniquely bridging rigorous theoretical guarantees with practical engineering applicability.

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Sequential Decision Making
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The Poisson compound decision problem is a classical problem in statistics, for which parametric and nonparametric empirical Bayes methodologies are available to estimate the Poisson's means in static or batch domains. In this paper, we consider the Poisson compound decision problem in a streaming or online domain. By relying on a quasi-Bayesian approach, often referred to as Newton's algorithm, we obtain sequential Poisson's mean estimates that are of easy evaluation, computationally efficient and with a constant computational cost as data increase, which is desirable for streaming data. Large sample asymptotic properties of the proposed estimates are investigated, also providing frequentist guarantees in terms of a regret analysis. We validate empirically our methodology, both on synthetic and real data, comparing against the most popular alternatives.

Problem

• Estimating Poisson means in streaming data
• Developing efficient sequential quasi-Bayesian estimation
• Ensuring asymptotic optimality with low computational cost

Innovation

• Sequential quasi-Bayesian approach for streaming data
• Computationally efficient Newton's algorithm
• Asymptotically optimal with vanishing regret