Variational Probabilistic Inference and the QMR-DT Network

Jaakkola, Tommi S.; Jordan, Michael I.

doi:10.1613/jair.583

Cited by 87 publications

(73 citation statements)

References 22 publications

(30 reference statements)

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“…Such constraints, which often arise in the setting of directed graphical models, require the general machinery of curved exponential families [74]. Although there have been specialized examples of variational methods applied to such families [122], there does not yet exist a general treatment of variational methods for curved exponential families.…”

Section: Discussionmentioning

confidence: 99%

Graphical Models, Exponential Families, and Variational Inference

Wainwright¹,

Jordan²

2007

FNT in Machine Learning

2,185

2,452

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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instancesincluding the key problems of computing marginals and modes of probability distributions -are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide variety of algorithms -among them sum-product, cluster variational methods, expectation-propagation, mean field methods, max-product and linear programming relaxation, as well as conic programming relaxations -can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.

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Section: Discussionmentioning

confidence: 99%

Graphical Models, Exponential Families, and Variational Inference

Wainwright¹,

Jordan²

2007

FNT in Machine Learning

2,185

2,452

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“…Among their many applications, Bayesian networks have been used for medical diagnosis (e.g., Kahn Jr. et al 1997;Jaakkola and Jordan 1999) and for inferring gene regulatory networks (e.g., Friedman et al 2000).…”

Section: Bayesian Networkmentioning

confidence: 99%

Predicting Gene Function From Patterns of Annotation

King¹,

Foulger²,

Dwight³

et al. 2003

Genome Res.

127

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The Gene Ontology (GO) Consortium has produced a controlled vocabulary for annotation of gene function that is used in many organism-specific gene annotation databases. This allows the prediction of gene function based on patterns of annotation. For example, if annotations for two attributes tend to occur together in a database, then a gene holding one attribute is likely to hold the other as well. We modeled the relationships among GO attributes with decision trees and Bayesian networks, using the annotations in the Saccharomyces Genome Database (SGD) and in FlyBase as training data. We tested the models using cross-validation, and we manually assessed 100 gene-attribute associations that were predicted by the models but that were not present in the SGD or FlyBase databases. Of the 100 manually assessed associations, 41 were judged to be true, and another 42 were judged to be plausible.[Detailed lists of hypotheses including the curators' comments on each hypothesis, are available at

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“…Bayesian formalism has been applied in diverse research fields. Numerous applications have been developed in physics [Jaynes, 1996, Neal, 1993, in artificial intelligence [Jaakkola and Jordan, 1999], as well as in mobile robotics [Thrun, 1998] and computer vision [Weiss and Adelson, 1998], and especially in parameter identification problems [Presse and Gautier, 1992].…”

Section: Introductionmentioning

confidence: 99%

The design and implementation of a Bayesian CAD modeler for robotic applications

Mekhnacha¹,

Mazer

Bessìère³

2001

Advanced Robotics

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We present a Bayesian CAD modeler for robotic applications. We address the problem of taking into account the propagation of geometric uncertainties when solving inverse geometric problems. The proposed method may be seen as a generalization of constraint-based approaches in which we explicitly model geometric uncertainties. Using our methodology, a geometric constraint is expressed as a probability distribution on the system parameters and the sensor measurements, instead of a simple equality or inequality. To solve geometric problems in this framework, we propose an original resolution method able to adapt to problem complexity. Using two examples, we show how to apply our approach by providing simulation results using our modeler.

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Variational Probabilistic Inference and the QMR-DT Network

Cited by 87 publications

References 22 publications

Graphical Models, Exponential Families, and Variational Inference

Graphical Models, Exponential Families, and Variational Inference

Predicting Gene Function From Patterns of Annotation

The design and implementation of a Bayesian CAD modeler for robotic applications

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