English

Completions to Discrete Probability Distributions in Log-linear Models

Statistics Theory 2024-12-04 v2 Algebraic Geometry Statistics Theory

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.

Keywords

Cite

@article{arxiv.2312.15154,
  title  = {Completions to Discrete Probability Distributions in Log-linear Models},
  author = {May Cai and Cecilie Olesen Recke and Thomas Yahl},
  journal= {arXiv preprint arXiv:2312.15154},
  year   = {2024}
}

Comments

This work was conducted as a part of the Algebraic Statistics and Our Changing World Program hosted by the Institute for Mathematical and Statistical Innovation (IMSI). 21 pages, 5 figures

R2 v1 2026-06-28T14:00:34.133Z