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Hidden Independence in Unstructured Probabilistic Models

Authors Antony Pearson , Manuel E. Lladser

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Subject Classification

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

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Abstract

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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.AofA.2020.23

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

Funding

  • Pearson, Antony: NSF Graduate Research Fellowship Program Grant No. 2016198773

Acknowledgements

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

References

  1. David Avis and Komei Fukuda. A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra. Discrete & Computational Geometry, 8(3):295-313, September 1992. URL: https://doi.org/10.1007/BF02293050.
  2. George B. Dantzig. Linear Programming and Extensions. United States Air Force Project RAND. The RAND Corporation, August 1963. URL: http://www.rand.org/pubs/reports/R366.html.
  3. Yuval Dekel. Number of real regular n x n (0,1) matrices modulo rows permutations, 2003. In: The On-line Encyclopedia of Integer Sequences. URL: https://oeis.org/A088389.
  4. Doug Hellmann. The Python 3 Standard Library by Example. Addison-Wesley Professional, 1 edition, 2017. Google Scholar
  5. Daphne Koller and Nir Friedman. Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning. The MIT Press, 2009. Google Scholar
  6. D. Kraft. A Software Package for Sequential Quadratic Programming. Deutsche Forschungs- und Versuchsanstalt für Luft- und Raumfahrt Köln: Forschungsbericht. Wiss. Berichtswesen d. DFVLR, 1988. Google Scholar
  7. Dinh Luc. Multiobjective linear programming: An Introduction. Springer, January 2015. URL: https://doi.org/10.1007/978-3-319-21091-9.
  8. Antony Pearson and Manuel E. Lladser. On Contamination of Symbolic Datasets. (Submitted). URL: http://arxiv.org/abs/2002.05592.
  9. M. Powell. A view of algorithms for optimization without derivatives. Mathematics TODAY, 43, January 2007. Google Scholar
  10. Alexander Schrijver. Theory of Linear and Integer Programming. Number Vol. 75 in Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, 1998. URL: https://search-ebscohost-com.colorado.idm.oclc.org/login.aspx?direct=true&db=nlebk&AN=17885&site=ehost-live&scope=site.
  11. Ben Taskar and Lise Getoor. Introduction to Statistical Relational Learning. Adaptive Computation and Machine Learning. The MIT Press, 2007. Google Scholar
  12. Miodrag Živković. Classification of small (0,1) matrices. Linear Algebra and its Applications, 414(1):310-346, 2006. URL: https://doi.org/10.1016/j.laa.2005.10.010.
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