Formal Limitations On The Measurement Of Mutual Information

INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 108(2020)

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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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Key words
mutual information,measurement
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