Formal Limitations on the Measurement of Mutual Information

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David McAllester, Karl Stratos ;
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:875-884, 2020.

Abstract

Measuring mutual information from finite data is difficult. Recent work has considered variational methods maximizing a lower bound. In this paper, we prove that serious statistical limitations are inherent to any method of measuring mutual information. More specifically, we show that any distribution-free high-confidence lower bound on mutual information estimated from N samples cannot be larger than O(ln N).

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