arXiv subjects

Johan Pensar

Publications and source records attributed to Johan Pensar.

23 records · Page 2Linked to original sources

arXiv2014

Stratified Gaussian Graphical Models

Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide certain forms of context-specific independence that are natural to consider from an applied perspective. Such independencies have been earlier introduced to generalize discrete graphical models and Bayesian networks into more flexible model families. Here we adapt the idea of context-specific independence to Gaussian graphical models by introducing a stratification of the Euclidean space such that a conditional independence may hold in certain segments but be absent elsewhere. It is shown that the stratified models define a curved exponential family, which retains considerable tractability for parameter estimation and model selection.

math.ST↗

arXiv2014

Marginal and simultaneous predictive classification using stratified graphical models

An inductive probabilistic classification rule must generally obey the principles of Bayesian predictive inference, such that all observed and unobserved stochastic quantities are jointly modeled and the parameter uncertainty is fully acknowledged through the posterior predictive distribution. Several such rules have been recently considered and their asymptotic behavior has been characterized under the assumption that the observed features or variables used for building a classifier are conditionally independent given a simultaneous labeling of both the training samples and those from an unknown origin. Here we extend the theoretical results to predictive classifiers acknowledging feature dependencies either through graphical models or sparser alternatives defined as stratified graphical models. We also show through experimentation with both synthetic and real data that the predictive classifiers based on stratified graphical models have consistently best accuracy compared with the predictive classifiers based on either conditionally independent features or on ordinary graphical models.

stat.ML↗

arXiv2013

Stratified Graphical Models - Context-Specific Independence in Graphical Models

Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and computer security, etc. Despite of their generic applicability and wide adoptance, the constraints imposed by undirected graphical models and Bayesian networks have also been recognized to be unnecessarily stringent under certain circumstances. This observation has led to the proposal of several generalizations that aim at more relaxed constraints by which the models can impose local or context-specific dependence structures. Here we consider an additional class of such models, termed as stratified graphical models. We develop a method for Bayesian learning of these models by deriving an analytical expression for the marginal likelihood of data under a specific subclass of decomposable stratified models. A non-reversible Markov chain Monte Carlo approach is further used to identify models that are highly supported by the posterior distribution over the model space. Our method is illustrated and compared with ordinary graphical models through application to several real and synthetic datasets.

stat.ML↗

arXiv2013

Labeled Directed Acyclic Graphs: a generalization of context-specific independence in directed graphical models

We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such that unrestricted label sets determine which edges can be deleted from the underlying directed acyclic graph (DAG) for a given context. Several properties of these models are derived, including a generalization of the concept of Markov equivalence classes. Efficient Bayesian learning of LDAGs is enabled by introducing an LDAG-based factorization of the Dirichlet prior for the model parameters, such that the marginal likelihood can be calculated analytically. In addition, we develop a novel prior distribution for the model structures that can appropriately penalize a model for its labeling complexity. A non-reversible Markov chain Monte Carlo algorithm combined with a greedy hill climbing approach is used for illustrating the useful properties of LDAG models for both real and synthetic data sets.

stat.ML↗

arXiv2013

Learning Chordal Markov Networks by Constraint Satisfaction

We investigate the problem of learning the structure of a Markov network from data. It is shown that the structure of such networks can be described in terms of constraints which enables the use of existing solver technology with optimization capabilities to compute optimal networks starting from initial scores computed from the data. To achieve efficient encodings, we develop a novel characterization of Markov network structure using a balancing condition on the separators between cliques forming the network. The resulting translations into propositional satisfiability and its extensions such as maximum satisfiability, satisfiability modulo theories, and answer set programming, enable us to prove optimal certain network structures which have been previously found by stochastic search.

cs.AI↗