We describe a graphical model for probabilistic relationships|an alternative tothe Bayesian network|called a dependency network. The graph of a dependency network, unlike aBayesian network, is potentially cyclic. The probability component of a dependency network, like aBayesian network, is a set of conditional distributions, one for each nodegiven its parents. We identify several basic properties of this representation and describe a computationally e cient procedure for learning the graph and probability components from data. We describe the application of this representation to probabilistic inference, collaborative ltering (the task of predicting preferences), and the visualization of acausal predictive relationships.

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Estimation of Distribution Algorithms (EDA) constitute an example of stochastics heuristics based on populations of individuals every of which encode the possible solutions to the optimization problem. These populations of individuals evolve in succesive generations as the search progresses -- organized in the same way as most evolutionary computation heuristics. In opposition to most evolutionary computation paradigms which consider the crossing and mutation operators as essential tools to generate new populations, EDA replaces those operators by the estimation and simulation of the joint probability distribution of the selected individuals. In this work, after making a review of the different approaches based on EDA for problems of combinatorial optimization as well as for problems of optimization in continuous domains, we propose new approaches based on the theory of probabilistic graphical models to solve problems in both domains. More precisely, we propose to adapt algorit...

We introduce the mixture of Gaussian processes (MGP) model which is useful for applications in which the optimal bandwidth of a map is input dependent. The MGP is derived from the mixture of experts model and can also be used for modeling general conditional probability densities. We discuss how Gaussian processes —in particular in form of Gaussian process classification, the support vector machine and the MGP model— can be used for quantifying the dependencies in graphical models. 1

Chain graphs are a natural generalization of directed acyclic graphs (DAGs) and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are a number of simple and apparently plausible, but ultimately fallacious interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to awed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated as the equilibrium distribution of dynamic models with feedback. These dynamic interpretations lead to a simple theory of intervention, extending the theory developed for DAGs. Finally, we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feedback in econometrics. Keywords: Causal model; cha...

Recommender systems use historical data on user preferences and other available data on users (for example, demographics) and items (for example, taxonomy) to predict items a new user might like. Applications of these methods include recommending items for purchase and personalizing the browsing experience on a web-site. Collaborative filtering methods have focused on using just the history of user preferences to make the recommendations.

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We present two algorithms for learning the structure of a Markov network from discrete data: GSMN and GSIMN. Both algorithms use statistical conditional independence tests on data to infer the structure by successively constraining the set of structures consistent with the results of these tests. GSMN is a natural adaptation of the Grow-Shrink algorithm of Margaritis and Thrun for learning the structure of Bayesian networks. GSIMN extends GSMN by additionally exploiting Pearl’s well-known properties of conditional independence relations to infer novel independencies from known independencies, thus avoiding the need to perform these tests. Experiments on artificial and real data sets show GSIMN can yield savings of up to 70 % with respect to GSMN, while generating a Markov network with comparable or in several cases considerably improved quality. In addition

We outline a representation for discrete multivariate distributions in terms of interventional potential functions that are globally normalized. This representation can be used to model the effects of interventions, and the independence properties encoded in this model can be represented as a directed graph that allows cycles. In addition to discussing inference and sampling with this representation, we give an exponential family parametrization that allows parameter estimation to be stated as a convex optimization problem; we also give a convex relaxation of the task of simultaneous parameter and structure learning using group ℓ1regularization. The model is evaluated on simulated data and intracellular flow cytometry data. 1

Bayesian networks have been successfully used to model joint probabilities in many cases. When dealing with continuous variables and nonlinear relationships neural networks can be used to model conditional densities as part of a Bayesian network. However, doing inference can then be computationally expensive. Also, information is implicitly passed backwards through neural networks, i.e. from their output to the input. Used in this "inverse" mode neural networks often perform suboptimal. We suggest a different type of model called Markov blanket model (MBM). Here the neural networks are used in the forward direction only. This gives advantages in speed and guarantees to match the performance of the underlying neural network on complete data. 1 Introduction Bayes nets (e.g. Heckerman (1995)) are models of the joint probability distribution of a set of variables fx i g N i=1 of the form p(x) = N Y i=1 p(x i jP i ): (1) where P i ` fx 1 ; : : : ; x i\Gamma1 g are the par...