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Learning parameters in discrete naive Bayes models by computing fibers of the parametrization map ; Wehenkel, Louis in NIPS ´08 Workshop: Algebraic and combinatorial methods in machine learning (2008, December 20) Discrete Naive Bayes models are usually defined parametrically with a map from a parameter space to a probability distribution space. First, we present two families of algorithms that compute the set of ... [more ▼] Discrete Naive Bayes models are usually defined parametrically with a map from a parameter space to a probability distribution space. First, we present two families of algorithms that compute the set of parameters mapped to a given discrete Naive Bayes distribution satisfying certain technical assumptions. Using these results, we then present two families of parameter learning algorithms that operate by projecting the distribution of observed relative frequencies in a dataset onto the discrete Naive Bayes model considered. They have nice convergence properties, but their computational complexity grows very quickly with the number of hidden classes of the model. [less ▲] Detailed reference viewed: 29 (1 ULg)Learning inclusion-optimal chordal graphs ; Wehenkel, Louis in Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence (UAI-08) (2008, July 09) Chordal graphs can be used to encode dependency models that are representable by both directed acyclic and undirected graphs. This paper discusses a very simple and efficient algorithm to learn the ... [more ▼] Chordal graphs can be used to encode dependency models that are representable by both directed acyclic and undirected graphs. This paper discusses a very simple and efficient algorithm to learn the chordal structure of a probabilistic model from data. The algorithm is a greedy hill-climbing search algorithm that uses the inclusion boundary neighborhood over chordal graphs. In the limit of a large sample size and under appropriate hypotheses on the scoring criterion, we prove that the algorithm will find a structure that is inclusion-optimal when the dependency model of the data-generating distribution can be represented exactly by an undirected graph. The algorithm is evaluated on simulated datasets. [less ▲] Detailed reference viewed: 8 (2 ULg)Modifying eigenvalue interactions near weak resonance ; ; Wehenkel, Louis in Proc. of International Symposium on Circuits and Systems (2004) In electric power system instabilities such as subsynchronous resonance or interarea oscillations, two complex modes can approach each other in frequency and then interact by changing damping so that one ... [more ▼] In electric power system instabilities such as subsynchronous resonance or interarea oscillations, two complex modes can approach each other in frequency and then interact by changing damping so that one of the modes becomes unstable. Selecting changes in parameters to minimize this interaction is difficult by trial and error. By analyzing the interaction as a perturbation of a weak resonance, we calculate sensitivities that indicate the parameters to be changed to minimize the interaction and stabilize the system. The method is illustrated with a simple example of two coupled linear oscillators. The use of sensitivity methods to change the type of the interaction is also demonstrated. [less ▲] Detailed reference viewed: 11 (1 ULg)On the construction of the inclusion boundary neighbourhood for markov equivalence classes of bayesian network structures ; Wehenkel, Louis in Proceedings of Uncertainty in Artificial Intelligence (2002) The problem of learning Markov equivalence classes of Bayesian network structures may be solved by searching for the maximum of a scoring metric in a space of these classes. This paper deals with the ... [more ▼] The problem of learning Markov equivalence classes of Bayesian network structures may be solved by searching for the maximum of a scoring metric in a space of these classes. This paper deals with the definition and analysis of one such search space. We use a theoretically motivated neighbourhood, the inclusion boundary, and represent equivalence classes by essential graphs. We show that this search space is connected and that the score of the neighbours can be evaluated incrementally. We devise a practical way of building this neighbourhood for an essential graph that is purely graphical and does not explicitely refer to the underlying independences. We find that its size can be intractable, depending on the complexity of the essential graph of the equivalence class. The emphasis is put on the potential use of this space with greedy hillclimbing search. [less ▲] Detailed reference viewed: 6 (1 ULg) |
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