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Activity Number:
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158
- Algebraic Methods in Statistics
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Type:
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Topic Contributed
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Date/Time:
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Monday, July 30, 2018 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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Abstract #329212
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Presentation
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Title:
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Totally Positive Exponential Families, Graphical Models, and Convex Optimization
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Author(s):
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Piotr Zwiernik*
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Companies:
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Universitat Pompeu Fabra
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Keywords:
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exponential families;
convex optimization;
total positivity;
graphical models
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Abstract:
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Probability distributions that are multivariate totally positive of order 2 (MTP2) appeared in the theory of positive dependence and in statistical physics through the celebrated FKG inequality. The MTP2 property is stable under marginalization, conditioning and it appears naturally in various probabilistic graphical models with hidden variables. Models of exponential families with the MTP2 property admit a unique maximum likelihood estimator. In the Gaussian case, the MLE exists also in high-dimensional settings, when p>>n, and it leads to sparse solutions.
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Authors who are presenting talks have a * after their name.
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