@proceedings {174, title = {Efficient and Robust Independence-Based Markov Network Structure Discovery.}, journal = {20th International Joint Conference of Artificial Inteliigence (IJCAI)}, year = {2007}, pages = {2431-2436 }, publisher = {Morgan Kaufmann Publishers Inc.}, address = {San Francisco, CA}, abstract = {

In this paper we introduce a novel algorithm for the induction of the Markov network structure of a domain from the outcome of conditional independence tests on data. Such algorithms work by successively restricting the set of possible structures until there is only a single structure consistent with the conditional independence tests executed. Existing independence-based algorithms have wellknown shortcomings, such as rigidly ordering the sequence of tests they perform, resulting in potential inefficiencies in the number of tests required, and committing fully to the test outcomes, resulting in lack of robustness in case of unreliable tests. We address both problems through a Bayesian particle filtering approach, which uses a population of Markov network structures to maintain the posterior probability distribution over them, given the outcomes of the tests performed. Instead of a fixed ordering, our approach greedily selects, at each step, the optimally informative from a pool of candidate tests according to information gain. In addition, it maintains multiple candidate structures weighed by posterior probability, which makes it more robust to errors in the test outcomes. The result is an approximate algorithm (due to the use of particle filtering) that is useful in domains where independence tests are uncertain (such as applications where little data is available) or expensive (such as cases of very large data sets and/or distributed data).

}, url = {http://www.aaai.org/Library/IJCAI/2007/ijcai07-391.php}, author = {Bromberg, Facundo and Margaritis, Dimitris} } @proceedings {176, title = {Efficient Markov network structure discovery using independence tests}, journal = {Proceedings of the SIAM Conference in Data Mining}, year = {2006}, pages = {141--152}, address = {Bethesda, Maryland, USA}, abstract = {

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{\textquoteright}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 to GSMN, we also compare GSIMN to a forward-chaining implementation, called GSIMN-FCH, that produces all possible conditional independence results by repeatedly applying Pearl{\textquoteright}s theorems on the known conditional independence tests. The results of this comparison show that GSIMN is nearly optimal in terms of the number of tests it can infer, under a fixed ordering of the tests performed.

}, isbn = {978-0-89871-611-5}, doi = {10.1137-1.9781611972764.13}, url = {http://epubs.siam.org/doi/abs/10.1137/1.9781611972764.13}, author = {Bromberg, Facundo and Margaritis, Dimitris and Honavar, Vasant} } @article {170, title = {Efficient Markov network discovery using particle filters}, journal = {Computational Intelligence}, volume = {25}, year = {2009}, month = {11/2009}, pages = {367{\textendash}394}, abstract = {

In this paper, we introduce an efficient independence-based algorithm for the induction of the Markov network (MN) structure of a domain from the outcomes of independence test conducted on data. Our algorithm utilizes a particle filter (sequential Monte Carlo) method to maintain a population of MN structures that represent the posterior probability distribution over structures, given the outcomes of the tests performed. This enables us to select, at each step, the maximally informative test to conduct next from a pool of candidates according to information gain, which minimizes the cost of the statistical tests conducted on data. This makes our approach useful in domains where independence tests are expensive, such as cases of very large data sets and/or distributed data. In addition, our method maintains multiple candidate structures weighed by posterior probability, which allows flexibility in the presence of potential errors in the test outcomes.

}, keywords = {graphical model structure learning, Markov networks, particle filters, sequential Monte Carlo}, doi = {10.1111/j.1467-8640.2009.00347.x}, url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1467-8640.2009.00347.x/abstract;jsessionid=C95A98B67CD44AF9ABF59B3B0CCAA979.f01t02?userIsAuthenticated=false\&deniedAccessCustomisedMessage=}, author = {Margaritis, Dimitris and Bromberg, Facundo} } @article {171, title = {Efficient Markov network structure discovery using independence tests}, journal = {Journal of Artificial Intelligence Research}, volume = {35}, year = {2009}, pages = {449{\textendash}484}, abstract = {

We present two algorithms for learning the structure of a Markov network from data: GSMN* and GSIMN. Both algorithms use statistical independence tests to infer the structure by successively constraining the set of structures consistent with the results of these tests. Until very recently, algorithms for structure learning were based on maximum likelihood estimation, which has been proved to be NP-hard for Markov networks due to the difficulty of estimating the parameters of the network, needed for the computation of the data likelihood. The independence-based approach does not require the computation of the likelihood, and thus both GSMN* and GSIMN can compute the structure efficiently (as shown in our experiments). GSMN* is an adaptation of the Grow-Shrink algorithm of Margaritis and Thrun for learning the structure of Bayesian networks. GSIMN extends GSMN* by additionally exploiting Pearls well-known properties of the conditional independence relation to infer novel independences from known ones, thus avoiding the performance of statistical tests to estimate them. To accomplish this efficiently GSIMN uses the Triangle theorem, also introduced in this work, which is a simplified version of the set of Markov axioms. Experimental comparisons on artificial and real-world data sets show GSIMN can yield significant savings with respect to GSMN*, while generating a Markov network with comparable or in some cases improved quality. We also compare GSIMN to a forward-chaining implementation, called GSIMN-FCH, that produces all possible conditional independences resulting from repeatedly applying Pearls theorems on the known conditional independence tests. The results of this comparison show that GSIMN, by the sole use of the Triangle theorem, is nearly optimal in terms of the set of independences tests that it infers.

}, doi = { 10.1613/jair.2773}, url = {http://www.jair.org/papers/paper2773.html}, author = {Bromberg, Facundo and Margaritis, Dimitris and Honavar, Vasant} }