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We propose algorithms for learning Markov boundaries from data without having to learn a Bayesian network first. We study their correctness, scalability and data efficiency. The last two properties are important because we aim to apply the algorithms to identify the minimal set of features that is needed for probabilistic classification in databases with… (More)

This paper proposes and evaluates the k-greedy equivalence search algorithm (KES) for learning Bayesian networks (BNs) from complete data. The main characteristic of KES is that it allows a trade-off between greediness and randomness, thus exploring different good local optima when run repeatedly. When greediness is set at maximum, KES corresponds to the… (More)

The application of the Bayesian Structural EM algorithm to learn Bayesian networks for clustering implies a search over the space of Bayesian network structures alternating between two steps: an optimization of the Bayesian network parameters (usually by means of the EM algorithm) and a structural search for model selection. In this paper, we propose to… (More)

We analyze two different feature selection problems: finding a minimal feature set optimal for classification (MINIMAL-OPTIMAL) vs. finding all features relevant to the target variable (ALL-RELEVANT). The latter problem is motivated by recent applications within bioinformatics, particularly gene expression analysis. For both problems, we identify classes of… (More)

We apply MCMC to approximately calculate (i) the ratio of directed acyclic graph (DAG) models to DAGs for up to 20 nodes, and (ii) the fraction of chain graph (CG) models that are neither undirected graph (UG) models nor DAG models for up to 13 nodes. Our results suggest that, for the numbers of nodes considered, (i) the ratio of DAG models to DAGs is not… (More)

In 2007, we applied MCMC to approximately calculate the ratio of essential graphs (EGs) to directed acyclic graphs (DAGs) for up to 20 nodes. In the present paper, we extend our previous work from 20 to 31 nodes. We also extend our previous work by computing the approximate ratio of connected EGs to connected DAGs, of connected EGs to EGs, and of connected… (More)

This paper deals with chain graphs under the alternative Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. We also show that the extension of Meek's conjecture to AMP chain graphs does not hold, which compromises the… (More)

We present a sound and complete graphical criterion for reading dependencies from the minimal undirected independence map G of a graphoid M that satisfies weak transitivity. Here, complete means that it is able to read all the dependencies in M that can be derived by applying the graphoid properties and weak transitivity to the dependencies used in the… (More)

Many optimization problems are what can be called globally multimodal, i.e., they present several global optima. Unfortunately, this is a major source of difficulties for most estimation of distribution algorithms, making their effectiveness and efficiency degrade, due to genetic drift. With the aim of overcoming these drawbacks for discrete globally… (More)

The covariance graph (aka bi-directed graph) of a probability distribution p is the undirected graph G where two nodes are adjacent iff their corresponding random variables are marginally dependent in p. * In this paper, we present a graphical criterion for reading dependencies from G, under the assumption that p satisfies the graphoid properties as well as… (More)