Hidden Independence in Unstructured Probabilistic Models

Authors Antony Pearson , Manuel E. Lladser

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Author Details

Antony Pearson
  • Department of Applied Mathematics, University of Colorado Boulder, CO, The United States
  • IQ Biology Program, BioFrontiers Institute, University of Colorado Boulder, CO, The United States
Manuel E. Lladser
  • Department of Applied Mathematics, University of Colorado Boulder, CO, The United States
  • Department of Computer Science (affiliate), University of Colorado Boulder, CO, The United States


We want to thank three anonymous referees for their careful reading and insightful comments that helped improve the quality of our manuscript.

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Antony Pearson and Manuel E. Lladser. Hidden Independence in Unstructured Probabilistic Models. In 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 159, pp. 23:1-23:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We describe a novel way to represent the probability distribution of a random binary string as a mixture having a maximally weighted component associated with independent (though not necessarily identically distributed) Bernoulli characters. We refer to this as the latent independent weight of the probabilistic source producing the string, and derive a combinatorial algorithm to compute it. The decomposition we propose may serve as an alternative to the Boolean paradigm of hypothesis testing, or to assess the fraction of uncorrupted samples originating from a source with independent marginal distributions. In this sense, the latent independent weight quantifies the maximal amount of independence contained within a probabilistic source, which, properly speaking, may not have independent marginal distributions.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Probabilistic representations
  • Mathematics of computing → Dimensionality reduction
  • Mathematics of computing → Discrete mathematics
  • Bayesian networks
  • contamination
  • latent weights
  • mixture models
  • independence
  • symbolic data


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