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Variational upper and lower bounds for probabilistic graphical models.

Ydo Wexler1, Dan Geiger

  • 1Computer Science Department, Technion, Haifa, Israel. ywex@cs.technion.ac.il

Journal of Computational Biology : a Journal of Computational Molecular Cell Biology
|July 26, 2008
PubMed
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We developed a novel approximation method for probabilistic phylogenetic models to overcome computational challenges. This technique provides reliable upper and lower bounds for likelihood computations, improving model parameter selection.

Area of Science:

  • Computational Biology
  • Phylogenetics
  • Statistical Modeling

Background:

  • Probabilistic phylogenetic models often require computationally intensive likelihood calculations.
  • Relaxing the site independence assumption in evolutionary models exacerbates these computational challenges.
  • Existing methods like variational inference offer lower bounds but can be insufficient for parameter selection.

Purpose of the Study:

  • To introduce a new approximation method for probabilistic models that provides both upper and lower bounds on the true likelihood.
  • To apply this method to address computational infeasibility in phylogenetic model parameter selection.
  • To offer a complementary approach to existing variational methods for likelihood approximation.

Main Methods:

  • Developed a novel approximation technique that guarantees to bound the true likelihood.

Related Experiment Videos

  • Applied the method to probabilistic phylogenetic models.
  • Utilized optimization strategies similar to variational methods to refine upper and lower bounds.

    • Main Results:

    • The approximation method was applied to aligned DNA sequences from human (CFTR gene) and homologous regions in eight mammals.
    • The computed bounds were found to be close to the true likelihood when exact computation was feasible.
    • Demonstrated tight approximation of the likelihood by showing proximity of upper and lower bounds when exact computation was infeasible.

    Conclusions:

    • The new approximation method effectively bounds the true likelihood for probabilistic phylogenetic models.
    • This method offers a viable solution for parameter selection in models with relaxed site independence assumptions.
    • The technique provides a reliable and computationally feasible alternative for likelihood approximation in phylogenetics.