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Two or more Bayesian network structures are Markov equivalent when the corresponding acyclic digraphs encode the same set of conditional independencies. Therefore, the search space of Bayesian network structures may be organized in equivalence classes, where each of them represents a different set of conditional independencies. The collection of sets of… (More)

Hierarchical latent class (HLC) models are tree-structured Bayesian networks where leaf nodes are observed while internal nodes are hidden. In earlier work, we have demonstrated in principle the possibility of reconstructing HLC models from data. In this paper, we address the scalability issue and develop a search-based algorithm that can efficiently learn… (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 search space of Bayesian Network struc tures is usually defined as Acyclic Directed Graphs (DAGs) and the search is done by lo cal transformations of DAGs. But the space of Bayesian Networks is ordered with respect to inclusion and it is natural to consider that a good search policy should take this into ac count. The first attempt to do this (Chick… (More)

Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the num ber of independent parameters. When hid den variables are present, however, standard dimension might no longer be appropriate. One should instead use… (More)

The inclusion problem deals with how to characterize (in graphical terms) whether all independence statements in the model in duced by a DAG K are in the model induced by a second DAG L. Meek (1997) conjec tured that this inclusion holds iff there exists a sequence of DAGs from L to K such that only certain 'legal' arrow reversal and 'legal' arrow adding… (More)

Hierarchical latent class (HLC) models are tree-structured Bayesian networks where leaf nodes are observed while internal nodes are latent. There are no theoretically well justified model selection criteria for HLC models in particular and Bayesian networks with latent nodes in general. Nonetheless, empirical studies suggest that the BIC score is a… (More)

We present a set covering algorithm and a compositional algorithm to describe sequences of www pages visits in click-stream data. The set covering algorithm utilizes the approach of rule specialization like the well known CN2 algorithm, the compositional algorithm is based on our original KEX algorithm, however both algorithms deal with sequences of events… (More)

Model complexity is an important factor to consider when selecting among Bayesian network models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e., the number of linearly independent network parameters. When latent variables are present, however, standard dimension is no longer appropriate and… (More)