High-dimensional prediction for count response via sparse exponential weights

The Tien Mai

doi:10.1111/stan.70013

2025-11-01

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The Tien Mai *

DOI：10.1111/stan.70013

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摘要

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Count data is prevalent in various fields such as ecology, medical and genomics research. In high-dimensional settings, where the number of features exceeds the sample size, feature selection becomes essential. While frequentist methods like Lasso have advanced in handling high-dimensional count data, Bayesian approaches remain underexplored with no theoretical results on prediction performance. This article introduces a novel probabilistic machine learning framework for high-dimensional count data prediction. We propose a pseudo-Bayesian method that integrates a scaled Student prior to promote sparsity and uses an exponential weight aggregation procedure. A key contribution is a novel risk measure tailored to count data prediction, with theoretical guarantees for prediction risk using PAC-Bayesian bounds. Our results include nonasymptotic oracle inequalities, demonstrating rate-optimal prediction error without prior knowledge of sparsity. We implement this approach efficiently using Langevin Monte Carlo method. Simulations and a real data application highlight the strong performance of our method compared to the Lasso in various settings.

Keyword:

count data

high-dimensional data

Langevin Monte Carlo

optimal rate

PAC-Bayes bounds

prediction error

sparsity