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44
Learning Bayesian networks: The combination of knowledge and statistical data
 Machine Learning
, 1995
"... We describe scoring metrics for learning Bayesian networks from a combination of user knowledge and statistical data. We identify two important properties of metrics, which we call event equivalence and parameter modularity. These properties have been mostly ignored, but when combined, greatly simpl ..."
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Cited by 924 (34 self)
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We describe scoring metrics for learning Bayesian networks from a combination of user knowledge and statistical data. We identify two important properties of metrics, which we call event equivalence and parameter modularity. These properties have been mostly ignored, but when combined, greatly simplify the encoding of a user’s prior knowledge. In particular, a user can express his knowledge—for the most part—as a single prior Bayesian network for the domain. 1
Using Bayesian networks to analyze expression data
 Journal of Computational Biology
, 2000
"... DNA hybridization arrays simultaneously measure the expression level for thousands of genes. These measurements provide a “snapshot ” of transcription levels within the cell. A major challenge in computational biology is to uncover, from such measurements, gene/protein interactions and key biologica ..."
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Cited by 753 (16 self)
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DNA hybridization arrays simultaneously measure the expression level for thousands of genes. These measurements provide a “snapshot ” of transcription levels within the cell. A major challenge in computational biology is to uncover, from such measurements, gene/protein interactions and key biological features of cellular systems. In this paper, we propose a new framework for discovering interactions between genes based on multiple expression measurements. This framework builds on the use of Bayesian networks for representing statistical dependencies. A Bayesian network is a graphbased model of joint multivariate probability distributions that captures properties of conditional independence between variables. Such models are attractive for their ability to describe complex stochastic processes and because they provide a clear methodology for learning from (noisy) observations. We start by showing how Bayesian networks can describe interactions between genes. We then describe a method for recovering gene interactions from microarray data using tools for learning Bayesian networks. Finally, we demonstrate this method on the S. cerevisiae cellcycle measurements of Spellman et al. (1998). Key words: gene expression, microarrays, Bayesian methods. 1.
Bayesian Network Classifiers
, 1997
"... Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier with strong assumptions of independence among features, called naive Bayes, is competitive with stateoftheart classifiers such as C4.5. This fact raises the question of whether a classifier with less restr ..."
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Cited by 607 (22 self)
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Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier with strong assumptions of independence among features, called naive Bayes, is competitive with stateoftheart classifiers such as C4.5. This fact raises the question of whether a classifier with less restrictive assumptions can perform even better. In this paper we evaluate approaches for inducing classifiers from data, based on the theory of learning Bayesian networks. These networks are factored representations of probability distributions that generalize the naive Bayesian classifier and explicitly represent statements about independence. Among these approaches we single out a method we call Tree Augmented Naive Bayes (TAN), which outperforms naive Bayes, yet at the same time maintains the computational simplicity (no search involved) and robustness that characterize naive Bayes. We experimentally tested these approaches, using problems from the University of California at Irvine repository, and compared them to C4.5, naive Bayes, and wrapper methods for feature selection.
Being Bayesian about network structure
 Machine Learning
, 2000
"... Abstract. In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model sel ..."
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Cited by 206 (5 self)
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Abstract. In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have nonnegligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior “landscape”. We present empirical results on synthetic and reallife datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a nonBayesian bootstrap approach.
A Guide to the Literature on Learning Probabilistic Networks From Data
, 1996
"... This literature review discusses different methods under the general rubric of learning Bayesian networks from data, and includes some overlapping work on more general probabilistic networks. Connections are drawn between the statistical, neural network, and uncertainty communities, and between the ..."
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Cited by 172 (0 self)
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This literature review discusses different methods under the general rubric of learning Bayesian networks from data, and includes some overlapping work on more general probabilistic networks. Connections are drawn between the statistical, neural network, and uncertainty communities, and between the different methodological communities, such as Bayesian, description length, and classical statistics. Basic concepts for learning and Bayesian networks are introduced and methods are then reviewed. Methods are discussed for learning parameters of a probabilistic network, for learning the structure, and for learning hidden variables. The presentation avoids formal definitions and theorems, as these are plentiful in the literature, and instead illustrates key concepts with simplified examples. Keywords Bayesian networks, graphical models, hidden variables, learning, learning structure, probabilistic networks, knowledge discovery. I. Introduction Probabilistic networks or probabilistic gra...
Discretizing Continuous Attributes While Learning Bayesian Networks
 In Proc. ICML
, 1996
"... We introduce a method for learning Bayesian networks that handles the discretization of continuous variables as an integral part of the learning process. The main ingredient in this method is a new metric based on the Minimal Description Length principle for choosing the threshold values for the dis ..."
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Cited by 67 (4 self)
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We introduce a method for learning Bayesian networks that handles the discretization of continuous variables as an integral part of the learning process. The main ingredient in this method is a new metric based on the Minimal Description Length principle for choosing the threshold values for the discretization while learning the Bayesian network structure. This score balances the complexity of the learned discretization and the learned network structure against how well they model the training data. This ensures that the discretization of each variable introduces just enough intervals to capture its interaction with adjacent variables in the network. We formally derive the new metric, study its main properties, and propose an iterative algorithm for learning a discretization policy. Finally, we illustrate its behavior in applications to supervised learning. 1 INTRODUCTION Bayesian networks provide efficient and effective representation of the joint probability distribution over a set ...
From Promoter Sequence to Expression: A Probabilistic Framework
, 2002
"... We present a probabilistic framework that models the process by which transcriptional binding explains the mRNA expression of different genes. Our joint probabilistic model unifies the two key components of this process: the prediction of gene regulation events from sequence motifs in the gene' ..."
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Cited by 57 (5 self)
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We present a probabilistic framework that models the process by which transcriptional binding explains the mRNA expression of different genes. Our joint probabilistic model unifies the two key components of this process: the prediction of gene regulation events from sequence motifs in the gene's promoter region, and the prediction of mRNA expression from combinations of gene regulation events in different settings. Our approach has several advantages. By learning promoter sequence motifs that are directly predictive of expression data, it can improve the identification of binding site patterns. It is also able to identify combinatorial regulation via interactions of different transcription factors. Finally, the general framework allows us to integrate additional data sources, including data from the recent binding localization assays. We demonstrate our approach on the cell cycle data of Spellman et al., combined with the binding localization information of Simon et al. We show that the learned model predicts expression from sequence, and that it identifies coherent coregulated groups with significant transcription factor motifs. It also provides valuable biological insight into the domain via these coregulated "modules" and the combinatorial regulation effects that govern their behavior.
Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network
 Proc. 1st IEEE Computer Society Bioinformatics Conference
, 2002
"... We propose a new statistical method for constructing a genetic network from microarray gene expression data by using a Bayesian network. An essential point of Bayesian network construction is in the estimation of the conditional distribution of each random variable. We consider fitting nonparametric ..."
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Cited by 38 (18 self)
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We propose a new statistical method for constructing a genetic network from microarray gene expression data by using a Bayesian network. An essential point of Bayesian network construction is in the estimation of the conditional distribution of each random variable. We consider fitting nonparametric regression models with heterogeneous error variances to the microarray gene expression data to capture the nonlinear structures between genes. A problem still remains to be solved in selecting an optimal graph, which gives the best representation of the system among genes. We theoretically derive a new graph selection criterion from Bayes approach in general situations. The proposed method includes previous methods based on Bayesian networks. We demonstrate the effectiveness of the proposed method through the analysis of Saccharomyces cerevisiae gene expression data newly obtained by disrupting 100 genes. 1.
Userexpertise modeling with empirically derived probabilistic implication networks
, 1996
"... ..."
Bayesian Network Classification with Continuous Attributes: Getting the Best of Both Discretization and Parametric Fitting
 In Proceedings of the International Conference on Machine Learning (ICML
, 1998
"... In a recent paper, Friedman, Geiger, and Goldszmidt [8] introduced a classifier based on Bayesian networks, called Tree Augmented Naive Bayes (TAN), that outperforms naive Bayes and performs competitively with C4.5 and other stateoftheart methods. This classifier has several advantages including ..."
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Cited by 28 (2 self)
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In a recent paper, Friedman, Geiger, and Goldszmidt [8] introduced a classifier based on Bayesian networks, called Tree Augmented Naive Bayes (TAN), that outperforms naive Bayes and performs competitively with C4.5 and other stateoftheart methods. This classifier has several advantages including robustness and polynomial computational complexity. One limitation of the TAN classifier is that it applies only to discrete attributes, and thus, continuous attributes must be prediscretized. In this paper, we extend TAN to deal with continuous attributes directly via parametric (e.g., Gaussians) and semiparametric (e.g., mixture of Gaussians) conditional probabilities. The result is a classifier that can represent and combine both discrete and continuous attributes. In addition, we propose a new method that takes advantage of the modeling language of Bayesian networks in order to represent attributes both in discrete and continuous form simultaneously, and use both versions in the classifi...