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arXiv · 2409.07325

Statistically Valid Information Bottleneck via Multiple Hypothesis Testing

Amirmohammad Farzaneh·Osvaldo Simeone
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Abstract

The information bottleneck (IB) problem is a widely studied framework in machine learning for extracting compressed features that are informative for downstream tasks. However, current approaches to solving the IB problem rely on a heuristic tuning of hyperparameters, offering no guarantees that the learned features satisfy information-theoretic constraints. In this work, we introduce a statistically valid solution to this problem, referred to as IB via multiple hypothesis testing (IB-MHT), which ensures that the learned features meet the IB constraints with high probability, regardless of the size of the available dataset. The proposed methodology builds on Pareto testing and learn-then-test (LTT), and it wraps around existing IB solvers to provide statistical guarantees on the IB constraints. We demonstrate the performance of IB-MHT on classical and deterministic IB formulations, including experiments on distillation of language models. The results validate the effectiveness of IB-MHT in outperforming conventional methods in terms of statistical robustness and reliability.

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Amirmohammad Farzaneh, Osvaldo Simeone. 2024-10-10. Statistically Valid Information Bottleneck via Multiple Hypothesis Testing. https://arxiv.org/abs/2409.07325

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