Uncertainty in Artificial Intelligence
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Lipschitz Parametrization of Probabilistic Graphical Models
Jean Honorio
Abstract:
We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the lp-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the Kullback-Leibler divergence that allows understanding methods that penalize the lp-norm of differences of parameters as the minimization of that upper bound. The expected log-likelihood is lower bounded by the negative lp-norm, which allows understanding the generalization ability of probabilistic models. The exponential of the negative ￿p-norm is involved in the lower bound of the Bayes error rate, which shows that it is reasonable to use parameters as features in algorithms that rely on metric spaces (e.g. classification, dimensionality reduction, clustering). Our results do not rely on specific algorithms for learning the structure or parameters. We show preliminary results for activity recognition and temporal segmentation.
Keywords:
Pages: 347-354
PS Link:
PDF Link: /papers/11/p347-honorio.pdf
BibTex:
@INPROCEEDINGS{Honorio11,
AUTHOR = "Jean Honorio ",
TITLE = "Lipschitz Parametrization of Probabilistic Graphical Models",
BOOKTITLE = "Proceedings of the Twenty-Seventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-11)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2011",
PAGES = "347--354"
}


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