The Principle of Uncertain Maximum Entropy

Kenneth Bogert; Matthew Kothe

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arXiv · 2305.09868

The Principle of Uncertain Maximum Entropy

Kenneth Bogert·Matthew Kothe

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Abstract

The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the available information be provided error-free (Jaynes, 1982). We relax this requirement using a memoryless communication channel as a framework to derive a new, more general principle. We show our new principle provides an upper bound on the entropy of the unknown distribution and the amount of information lost due to the use of a given communications channel is unknown unless the unknown distribution's entropy is also known. Using our new principle we provide a new interpretation of the classic principle and experimentally show its performance relative to the classic principle and some other generally applicable solutions.

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Kenneth Bogert, Matthew Kothe. 2023-05-17. The Principle of Uncertain Maximum Entropy. https://arxiv.org/abs/2305.09868

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