We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the L_p-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the Kullback-Leibler di vergence that allows understanding methods that penalize the L_p-norm of differences of pa rameters as the minimization of that upper bound. The expected log-likelihood is lower bounded by the negative L_p,-norm, which al lows understanding the generalization ability of probabilistic models. The exponential of the negative L_p-norm is involved in the lower bound of the Bayes error rate, which shows that it is reasonable to use parameters as fea tures in algorithms that rely on metric spaces (e.g. classification, dimensionality reduction, clustering). Our results do not rely on spe cific algorithms for learning the structure or parameters. We show preliminary results for activity recognition and temporal segmenta tion.
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