March 2010

We introduce a nonparametric representation for graphical model on trees which expresses marginals as Hilbert space embeddings and conditionals as embedding operators. This formulation allows us to define a graphical model solely on the basis of the feature space representation of its variables. Thus, this nonparametric model can be applied to general domains where kernels are defined, handling challenging cases such as discrete variables whose domains are huge, or very complex, non-Gaussian continuous distributions. We also derive kernel […]

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Universal kernels have been shown to play an important role in the achievability of the Bayes risk by many kernel-based algorithms that include binary classification, regression, etc. In this paper, we propose a notion of universality that generalizes the notions introduced by Steinwart and Micchelli et al. and study the necessary and sufficient conditions for a kernel to be universal. We show that all these notions of universality are closely linked to the injective embedding of a certain […]

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Estimating the conditional mean of an input-output relation is the goal of regression. However, regression analysis is not sufficiently informative if the conditional distribution has multi-modality, is highly asymmetric, or contains heteroscedastic noise. In such scenarios, estimating the conditional distribution itself would be more useful. In this paper, we propose a novel method of conditional density estimation that is suitable for multi-dimensional continuous variables. The basic idea of the proposed method is to express the conditional density in […]

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Contrastive Divergence (CD) is a popular method for estimating the parameters of Markov Random Fields (MRFs) by rapidly approximating an intractable term in the gradient of the log probability. Despite CD’s empirical success, little is known about its theoretical convergence properties. In this paper, we analyze the CD$_1$ update rule for Restricted Boltzmann Machines (RBMs) with binary variables. We show that this update is not the gradient of any function, and construct a counterintuitive “regularization function” that causes […]

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Probabilistic models of the performance of computer systems are useful both for predicting system performance in new conditions, and for diagnosing past performance problems. The most popular performance models are networks of queues. However, no current methods exist for parameter estimation or inference in networks of queues with missing data. In this paper, we present a novel viewpoint that combines queueing networks and graphical models, allowing Markov chain Monte Carlo to be applied. We demonstrate the effectiveness of […]

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The goal of sufficient dimension reduction in supervised learning is to find the low dimensional subspace of input features that is “sufficient” for predicting output values. In this paper, we propose a novel sufficient dimension reduction method using a squared-loss variant of mutual information as a dependency measure. We utilize an analytic approximator of squared-loss mutual information based on density ratio estimation, which is shown to possess suitable convergence properties. We then develop a natural gradient algorithm for […]

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There is a growing interest in building probabilistic models with high order potentials (HOPs), or interactions, among discrete variables. Message passing inference in such models generally takes time exponential in the size of the interaction, but in some cases maximum a posteriori (MAP) inference can be carried out efficiently. We build upon such results, introducing two new classes, including composite HOPs that allow us to flexibly combine tractable HOPs using simple logical switching rules. We present efficient message […]

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Preface to the Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics May 13-15, 2010, Chia Laguna Resort, Sardinia, Italy.

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Hartigan’s method for $k$-means clustering is the following greedy heuristic: select a point, and optimally reassign it. This paper develops two other formulations of the heuristic, one leading to a number of consistency properties, the other showing that the data partition is always quite separated from the induced Voronoi partition. A characterization of the volume of this separation is provided. Empirical tests verify not only good optimization performance relative to Lloyd’s method, but also good running time.

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With the goal to generate more scalable algorithms with higher efficiency and fewer open parameters, reinforcement learning (RL) has recently moved towards combining classical techniques from optimal control and dynamic programming with modern learning techniques from statistical estimation theory. In this vein, this paper suggests to use the framework of stochastic optimal control with path integrals to derive a novel approach to RL with parametrized policies. While solidly grounded in value function estimation and optimal control based on […]

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