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Efficient Structure Learning and Sampling of Bayesian Networks.
Jack Kuipers,Polina Suter,Giusi Moffa +2 more
- 21 Mar 2018
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TL;DR: This work synthesises constraint based methods that perform conditional independence tests to exclude edges and score and search approaches which explore the DAG space with greedy or MCMC schemes in a novel hybrid method which reduces the complexity of MCMC approaches to that of a constraint based method.
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Abstract: Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed acyclic graph (DAG) is highly challenging mainly due to the vast number of possible networks. Efforts have focussed on two fronts: constraint based methods that perform conditional independence tests to exclude edges and score and search approaches which explore the DAG space with greedy or MCMC schemes. Here we synthesise these two fields in a novel hybrid method which reduces the complexity of MCMC approaches to that of a constraint based method. Individual steps in the MCMC scheme only require simple table lookups so that very long chains can be efficiently obtained. Furthermore, the scheme includes an iterative procedure to correct for errors from the conditional independence tests. The algorithm not only offers markedly superior performance to alternatives, but DAGs can also be sampled from the posterior distribution enabling full Bayesian modelling averaging for much larger Bayesian networks.
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Probabilistic Graphical Models
Daphne Koller,Nir Friedman +1 more
- 31 Jul 2009
Abstract: Probabilistic graphical models provide a flexible framework for modeling large, complex, heterogeneous collections of random variables. Graphs are used to decompose multivariate, joint distributions into a set of local interactions among small subsets of variables. These local relationships produce conditional independencies which lead to efficient learning and inference algorithms. Moreover, their modular structure provides an intuitive language for expressing domain-specific knowledge, and facilitates the transfer of modeling advances to new applications. After a brief introduction to their representational power, this course will provide a comprehensive survey of state-of-the-art methods for statistical learning and inference in graphical models. Our primary focus will be variational methods, which adapt tools from optimization theory to develop efficient, possibly approximate, inference algorithms. We will also discuss a complementary family of Monte Carlo methods, based on stochastic simulation. Many course readings will be drawn from the draft textbook An Introduction to Probabilistic Graphical Models, in preparation by Michael Jordan. Advanced topics will be supported by tutorial and survey articles, and illustrated with state-of-the-art research results and applications. Overall grades will be assigned based on homework assignments combining statistical analysis and implementation of learning algorithms, as well as a final research project involving probabilistic graphical models. Students who took CSCI 2950-P in the Fall of 2011 may repeat for credit, as the topic has changed.
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A tutorial on bayesian networks for psychopathology researchers.
TL;DR: This tutorial aims to introduce Bayesian Networks to identify admissible causal relationships in cross-sectional data, as well as how to estimate these models in R through three algorithm families with an empirical example data set of depressive symptoms.
•Posted Content
Efficient Sampling and Structure Learning of Bayesian Networks
TL;DR: A novel hybrid method which reduces the complexity of MCMC approaches to that of a constraint-based method and offers markedly superior performance to alternatives, particularly because DAGs can also be sampled from the posterior distribution, enabling full Bayesian model averaging for much larger Bayesian networks.
70
A Better Mechanistic Understanding of Big Data through an Order Search Using Causal Bayesian Networks
TL;DR: A practical causal discovery algorithm using causal Bayesian networks to gain a better understanding of the underlying mechanistic process that generated the data and shows that incorporating order information provides a better mechanistic understanding even when hidden confounded causes are present.
4
•Posted Content
A Birth and Death Process for Bayesian Network Structure Inference
Dale Jennings,J. N. Corcoran +1 more
TL;DR: In this paper, the authors model the appearance and disappearance of edges as a birth and death process and compare their approach to the popular Metropolis-Hastings search strategy, and give empirical evidence that the birth-and-death process has superior mixing properties.
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References
Causality: models, reasoning, and inference
TL;DR: The art and science of cause and effect have been studied in the social sciences for a long time as mentioned in this paper, see, e.g., the theory of inferred causation, causal diagrams and the identification of causal effects.
14.9K
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Causation, prediction, and search
Peter Spirtes,Clark Glymour,Richard Scheines +2 more
- 01 Jan 1993
TL;DR: The authors axiomatize the connection between causal structure and probabilistic independence, explore several varieties of causal indistinguishability, formulate a theory of manipulation, and develop asymptotically reliable procedures for searching over equivalence classes of causal models.
Using Bayesian networks to analyze expression data
TL;DR: A new framework for discovering interactions between genes based on multiple expression measurements is proposed and a method for recovering gene interactions from microarray data is described using tools for learning Bayesian networks.
3.7K
Causation, Prediction, and Search
TL;DR: Although Testing Statistical Hypotheses of Equivalence has some weaknesses, it is a useful reference for those interested in the question of equivalence testing, particularly in biological applications.
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Using Bayesian networks to analyze expression data
Nir Friedman,Michal Linial,Iftach Nachman,Dana Pe'er +3 more
- 08 Apr 2000
TL;DR: This paper proposes a new framework for discovering interactions between genes based on multiple expression measurements, and presents an efficient algorithm capable of learning such networks and statistical method to assess confidence in their features.