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arXiv · 2312.15154

Completions to Discrete Probability Distributions in Log-linear Models

May Cai·Cecilie Olesen Recke·Thomas Yahl
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Abstract

Completion problems, of recovering a point from a set of observed coordinates, are abundant in applications to image reconstruction, phylogenetics, and data science. We consider a completion problem coming from algebraic statistics: to describe the completions of a point to a probability distribution lying in a given log-linear model. When there are finitely many completions, we show that these points either have a unique completion or two completions to the log-linear model depending on the set of observed coordinates. We additionally describe the region of points which have a completion to the log-linear model.

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May Cai, Cecilie Olesen Recke, Thomas Yahl. 2023-12-23. Completions to Discrete Probability Distributions in Log-linear Models. https://doi.org/10.2140/astat.2024.15.225

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