Results 11  20
of
64
Data Analysis with Bayesian Networks: A Bootstrap Approach
, 1999
"... In recent years there has been significant progress in algorithms and methods for inducing Bayesian networks from data. However, in complex data analysis problems, we need to go beyond being satisfied with inducing networks with high scores. We need to provide confidence measures on features o ..."
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Cited by 48 (7 self)
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In recent years there has been significant progress in algorithms and methods for inducing Bayesian networks from data. However, in complex data analysis problems, we need to go beyond being satisfied with inducing networks with high scores. We need to provide confidence measures on features of these networks: Is the existence of an edge between two nodes warranted? Is the Markov blanket of a given node robust? Can we say something about the ordering of the variables? We should be able to address these questions, even when the amount of data is not enough to induce a high scoring network. In this paper we propose Efron's Bootstrap as a computationally efficient approach for answering these questions. In addition, we propose to use these confidence measures to induce better structures from the data, and to detect the presence of latent variables.
Nonlinear causal discovery with additive noise models
"... The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuousvalued data linear acyclic causal models with additive noise are often used because these models are well understood and there are wellknown methods to fit them to data. In ..."
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Cited by 35 (16 self)
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The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuousvalued data linear acyclic causal models with additive noise are often used because these models are well understood and there are wellknown methods to fit them to data. In reality, of course, many causal relationships are more or less nonlinear, raising some doubts as to the applicability and usefulness of purely linear methods. In this contribution we show that in fact the basic linear framework can be generalized to nonlinear models. In this extended framework, nonlinearities in the datagenerating process are in fact a blessing rather than a curse, as they typically provide information on the underlying causal system and allow more aspects of the true datagenerating mechanisms to be identified. In addition to theoretical results we show simulations and some simple real data experiments illustrating the identification power provided by nonlinearities. 1
Discriminative, Generative and Imitative Learning
, 2002
"... I propose a common framework that combines three different paradigms in machine learning: generative, discriminative and imitative learning. A generative probabilistic distribution is a principled way to model many machine learning and machine perception problems. Therein, one provides domain specif ..."
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Cited by 34 (1 self)
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I propose a common framework that combines three different paradigms in machine learning: generative, discriminative and imitative learning. A generative probabilistic distribution is a principled way to model many machine learning and machine perception problems. Therein, one provides domain specific knowledge in terms of structure and parameter priors over the joint space of variables. Bayesian networks and Bayesian statistics provide a rich and flexible language for specifying this knowledge and subsequently refining it with data and observations. The final result is a distribution that is a good generator of novel exemplars.
Constructing Bayesian Network Models of Gene Expression Networks from Microarray Data
, 2000
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Beyond covariation: Cues to causal structure
 In A. Gopnik & L. Schulz (Eds.), Causal learning: Psychology, philosophy, and computation
, 2006
"... computation. In preparation. Address for correspondence: ..."
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Cited by 22 (6 self)
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computation. In preparation. Address for correspondence:
Bayesian Network Analysis of Signaling Networks: A Primer
, 2005
"... Highthroughput proteomic data can be used to reveal the connectivity of signaling networks and the influences between signaling molecules. We present a primer on the use of Bayesian networks for this task. Bayesian networks have been successfully used to derive causal influences among biological si ..."
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Cited by 21 (0 self)
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Highthroughput proteomic data can be used to reveal the connectivity of signaling networks and the influences between signaling molecules. We present a primer on the use of Bayesian networks for this task. Bayesian networks have been successfully used to derive causal influences among biological signaling molecules (for example, in the analysis of intracellular multicolor flow cytometry). We discuss ways to automatically derive a Bayesian network model from proteomic data and to interpret the resulting model.
Robust independence testing for constraintbased learning of causal structure
 In UAI
, 2003
"... This paper considers a method that combines ideas from Bayesian learning, Bayesian network inference, and classical hypothesis testing to produce a more reliable and robust test of independence for constraintbased (CB) learning of causal structure. Our method produces a smoothed contingency table NX ..."
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Cited by 13 (1 self)
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This paper considers a method that combines ideas from Bayesian learning, Bayesian network inference, and classical hypothesis testing to produce a more reliable and robust test of independence for constraintbased (CB) learning of causal structure. Our method produces a smoothed contingency table NXY Z that can be used with any test of independence that relies on contingency table statistics. NXY Z can be calculated in the same asymptotic time and space required to calculate a standard contingency table, allows the specification of a prior distribution over parameters, and can be calculated when the database is incomplete. We provide theoretical justification for the procedure, and with synthetic data we demonstrate its benefits empirically over both a CB algorithm using the standard contingency table, and over a greedy Bayesian algorithm. We show that, even when used with noninformative priors, it results in better recovery of structural features and it produces networks with smaller KLDivergence, especially as the number of nodes increases or the number of records decreases. Another benefit is the dramatic reduction in the probability that a CB algorithm will stall during the search, providing a remedy for an annoying problem plaguing CB learning when the database is small. 1
Evaluating the Effect of Perturbations in Reconstructing Network Topologies
 In Proc. 3rd Intl. Wk. on Distrib. Stat. Computing
, 2003
"... Many different Bayesian network models have been suggested... ..."
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Cited by 12 (8 self)
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Many different Bayesian network models have been suggested...
Causal inference using the algorithmic Markov condition
, 2008
"... Inferring the causal structure that links n observables is usually basedupon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only single observations are present. We develop a theory how to g ..."
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Cited by 11 (11 self)
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Inferring the causal structure that links n observables is usually basedupon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when only single observations are present. We develop a theory how to generate causal graphs explaining similarities between single objects. To this end, we replace the notion of conditional stochastic independence in the causal Markov condition with the vanishing of conditional algorithmic mutual information anddescribe the corresponding causal inference rules. We explain why a consistent reformulation of causal inference in terms of algorithmic complexity implies a new inference principle that takes into account also the complexity of conditional probability densities, making it possible to select among Markov equivalent causal graphs. This insight provides a theoretical foundation of a heuristic principle proposed in earlier work. We also discuss how to replace Kolmogorov complexity with decidable complexity criteria. This can be seen as an algorithmic analog of replacing the empirically undecidable question of statistical independence with practical independence tests that are based on implicit or explicit assumptions on the underlying distribution. email: