On the Effectiveness of Hybrid Mutual Information Estimation

Marco Federici; David Ruhe; Patrick Forré

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arXiv · 2306.00608

On the Effectiveness of Hybrid Mutual Information Estimation

Marco Federici·David Ruhe·Patrick Forré

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Abstract

Estimating the mutual information from samples from a joint distribution is a challenging problem in both science and engineering. In this work, we realize a variational bound that generalizes both discriminative and generative approaches. Using this bound, we propose a hybrid method to mitigate their respective shortcomings. Further, we propose Predictive Quantization (PQ): a simple generative method that can be easily combined with discriminative estimators for minimal computational overhead. Our propositions yield a tighter bound on the information thanks to the reduced variance of the estimator. We test our methods on a challenging task of correlated high-dimensional Gaussian distributions and a stochastic process involving a system of free particles subjected to a fixed energy landscape. Empirical results show that hybrid methods consistently improved mutual information estimates when compared to the corresponding discriminative counterpart.

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Marco Federici, David Ruhe, Patrick Forré. 2023-06-02. On the Effectiveness of Hybrid Mutual Information Estimation. https://arxiv.org/abs/2306.00608

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