Learning Markov Network Structures Constrained by Context-Specific Independences

This work focuses on learning the structure of Markov networks from data. Markov networks are parametric models for compactly representing complex probability distributions. These models are composed by: a structure and numerical weights, where the structure describes independences that hold in the distribution. Depending on which is the goal of structure learning, learning algorithms can be divided into: density estimation algorithms, where structure is learned for answering inference queries; and knowledge discovery algorithms, where structure is learned for describing independences qualitatively. The latter algorithms present an important limitation for describing independences because they use a single graph; a coarse grain structure representation which cannot represent flexible independences. For instance, context-specific independences cannot be described by a single graph. To overcome this limitation, this work proposes a new alternative representation named canonical model as well as the CSPC algorithm; a novel knowledge discovery algorithm for learning canonical models by using context-specific independences as constraints. On an extensive empirical evaluation, CSPC learns more accurate structures than state-of-the-art density estimation and knowledge discovery algorithms. Moreover, for answering inference queries, our approach obtains competitive results against density estimation algorithms, significantly outperforming knowledge discovery algorithms.Fil: Edera, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Tecnológica Nacional. Facultad Regional Mendoza. Departamento de Sistemas de Información; ArgentinaFil: Schluter, Federico Enrique Adolfo. Universidad Tecnológica Nacional. Facultad Regional Mendoza. Departamento de Sistemas de Información; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; ArgentinaFil: Bromberg, Facundo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Tecnológica Nacional. Facultad Regional Mendoza. Departamento de Sistemas de Información; Argentin

Blankets Joint Posterior score for learning Markov network structures

Markov networks are extensively used to model complex sequential, spatial, and relational interactions in a wide range of fields. By learning the Markov network independence structure of a domain, more accurate joint probability distributions can be obtained for inference tasks or, more directly, for interpreting the most significant relations among the variables. Recently, several researchers have investigated techniques for automatically learning the structure from data by obtaining the probabilistic maximum-a-posteriori structure given the available data. However, all the approximations proposed decompose the posterior of the whole structure into local sub-problems, by assuming that the posteriors of the Markov blankets of all the variables are mutually independent. In this work, we propose a scoring function for relaxing such assumption. The Blankets Joint Posterior score computes the joint posterior of structures as a joint distribution of the collection of its Markov blankets. Essentially, the whole posterior is obtained by computing the posterior of the blanket of each variable as a conditional distribution that takes into account information from other blankets in the network. We show in our experimental results that the proposed approximation can improve the sample complexity of state-of-the-art competitors when learning complex networks, where the independence assumption between blanket variables is clearly incorrect.Fil: Schluter, Federico Enrique Adolfo. Universidad Tecnológica Nacional. Facultad Regional de Mendoza; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Strappa Figueroa, Yanela Daiana. Universidad Tecnológica Nacional. Facultad Regional de Mendoza; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Milone, Diego Humberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hídricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; ArgentinaFil: Bromberg, Facundo. Universidad Tecnológica Nacional. Facultad Regional de Mendoza; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin