Learning probabilistic decision graphs

Probabilistic Decision Graphs (PDGs) are probabilistic graphical models that represent a factorisation of a discrete joint probability distribution using a "decision graph"-like structure over local marginal parameters. The structure of a PDG enables the model to capture some context specific independence relations that are not representable in the structure of more commonly used graphical models such as Bayesian networks and Markov networks. This sometimes makes operations in PDGs more efficient than in alternative models. PDGs have previously been defined only in the discrete case, assuming a multinomial joint distribution over the variables in the model. We extend PDGs to incorporate continuous variables, by assuming a Conditional Gaussian (CG) joint distribution. We also show how inference can be carried out in an efficient way.

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“…We will also study the problem of inducing CG-PDGs from data, that so fas has been successfully addressed for discrete PDGs [17,19].…”

Section: Discussionmentioning

confidence: 99%

“…In our example, this simply CG-PDG model and subsequently simplifying the obtained CG-PDG model by merging nodes in the structure. We will review the structural operation of merging nodes used in [17] which is defined only for nodes representing discrete random variables.…”

Section: Examplementioning

confidence: 99%

Modelling and inference with Conditional Gaussian Probabilistic Decision Graphs

Nielsen

Gámez

Salmerón

2012

International Journal of Approximate Reasoning

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“…Previous comparative studies have demonstrated the strength of the PDG model as a secondary structure in probability estimation . In the study of Jaeger et al (2004), a PDG is learned from a Junction Tree model and thereafter a series of merging operations is applied. These operations effectively remove redundant parameters and parameters with little or no data-support.…”

Section: Learning the Pdg Classifiermentioning

confidence: 99%

“…Probabilistic decision graphs (PDGs) constitute a class of probabilistic graphical models that naturally capture certain context specific independencies (Boutilier et al, 1996) that are not easily represented by other graphical models (Jaeger, 2004;Jaeger et al, 2006). This means that the PDG model can capture some distributions with fewer parameters than classical models, which in some situations leads to a model less prone to over-fitting.…”

Section: Introductionmentioning

confidence: 99%

Supervised classification using probabilistic decision graphs

Nielsen

Rumí

Salmerón

2009

Computational Statistics & Data Analysis

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A new model for supervised classification based on probabilistic decision graphs is introduced. A probabilistic decision graph (PDG) is a graphical model that efficiently captures certain context specific independencies that are not easily represented by other graphical models traditionally used for classification, such as the Naïve Bayes (NB) or Classification Trees (CT). This means that the PDG model can capture some distributions using fewer parameters than classical models. Two approaches for constructing a PDG for classification are proposed. The first is to directly construct the model from a dataset of labelled data, while the second is to transform a previously obtained Bayesian classifier into a PDG model that can then be refined. These two approaches are compared with a wide range of classical approaches to the supervised classification problem on a number of both real world databases and artificially generated data.

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“…Recently, there has been work by Lowd and Domingos (2008) which learns a Bayes net while directly penalizing the complexity of the associated arithmetic circuit. Another approach for representing probability distributions which particularly takes benefit of context specific independence is based on Probabilistic Decision Graphs (PDG) (Jaeger et al 2006). However, similar to BN, PDG are not guaranteed to be efficient in the most general cases.…”

Section: Related Workmentioning

confidence: 99%

Learning multi-linear representations of distributions for efficient inference

Roth

Samdani

2009

Mach Learn

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We examine the class of multi-linear representations (MLR) for expressing probability distributions over discrete variables. Recently, MLR have been considered as intermediate representations that facilitate inference in distributions represented as graphical models.We show that MLR is an expressive representation of discrete distributions and can be used to concisely represent classes of distributions which have exponential size in other commonly used representations, while supporting probabilistic inference in time linear in the size of the representation. Our key contribution is presenting techniques for learning bounded-size distributions represented using MLR, which support efficient probabilistic inference. We demonstrate experimentally that the MLR representations we learn support accurate and very efficient inference.

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Learning probabilistic decision graphs

Cited by 24 publications

References 9 publications

Modelling and inference with Conditional Gaussian Probabilistic Decision Graphs

Modelling and inference with Conditional Gaussian Probabilistic Decision Graphs

Supervised classification using probabilistic decision graphs

Learning multi-linear representations of distributions for efficient inference

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