Results 1  10
of
49
Learning Bayesian network structure from massive datasets: The “sparse candidate” algorithm
, 1999
"... Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem using standard heuristic search techniques. Since the searc ..."
Abstract

Cited by 181 (10 self)
 Add to MetaCart
Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem using standard heuristic search techniques. Since the search space is extremely large, such search procedures can spend most of the time examining candidates that are extremely unreasonable. This problem becomes critical when we deal with data sets that are large either in the number of instances, or the number of attributes. In this paper, we introduce an algorithm that achieves faster learning by restricting the search space. This iterative algorithm restricts the parents of each variable to belong to a small subset of candidates. We then search for a network that satisfies these constraints. The learned network is then used for selecting better candidates for the next iteration. We evaluate this algorithm both on synthetic and reallife data. Our results show that it is significantly faster than alternative search procedures without loss of quality in the learned structures. 1
Learning Bayesian Networks is NPHard
, 1994
"... Algorithms for learning Bayesian networks from data have two components: a scoring metric and a search procedure. The scoring metric computes a score reflecting the goodnessoffit of the structure to the data. The search procedure tries to identify network structures with high scores. Heckerman et ..."
Abstract

Cited by 130 (2 self)
 Add to MetaCart
Algorithms for learning Bayesian networks from data have two components: a scoring metric and a search procedure. The scoring metric computes a score reflecting the goodnessoffit of the structure to the data. The search procedure tries to identify network structures with high scores. Heckerman et al. (1994) introduced a Bayesian metric, called the BDe metric, that computes the relative posterior probability of a network structure given data. They show that the metric has a property desireable for inferring causal structure from data. In this paper, we show that the problem of deciding whether there is a Bayesian networkamong those where each node has at most k parentsthat has a relative posterior probability greater than a given constant is NPcomplete, when the BDe metric is used. 1 Introduction Recently, many researchers have begun to investigate methods for learning Bayesian networks, including Bayesian methods [Cooper and Herskovits, 1991, Buntine, 1991, York 1992, Spiegel...
The maxmin hillclimbing bayesian network structure learning algorithm
 Machine Learning
, 2006
"... Abstract. We present a new algorithm for Bayesian network structure learning, called MaxMin HillClimbing (MMHC). The algorithm combines ideas from local learning, constraintbased, and searchandscore techniques in a principled and effective way. It first reconstructs the skeleton of a Bayesian n ..."
Abstract

Cited by 76 (7 self)
 Add to MetaCart
Abstract. We present a new algorithm for Bayesian network structure learning, called MaxMin HillClimbing (MMHC). The algorithm combines ideas from local learning, constraintbased, and searchandscore techniques in a principled and effective way. It first reconstructs the skeleton of a Bayesian network and then performs a Bayesianscoring greedy hillclimbing search to orient the edges. In our extensive empirical evaluation MMHC outperforms on average and in terms of various metrics several prototypical and stateoftheart algorithms, namely the PC, Sparse Candidate, Three Phase Dependency Analysis, Optimal Reinsertion, Greedy Equivalence Search, and Greedy Search. These are the first empirical results simultaneously comparing most of the major Bayesian network algorithms against each other. MMHC offers certain theoretical advantages, specifically over the Sparse Candidate algorithm, corroborated by our experiments. MMHC and detailed results of our study are publicly available at
Asymptotic model selection for directed networks with hidden variables
, 1996
"... We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as our extension punishes the complexity of a ..."
Abstract

Cited by 49 (15 self)
 Add to MetaCart
We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as our extension punishes the complexity of a model according to the dimension of its parameters. We argue that the dimension of a Bayesian network with hidden variables is the rank of the Jacobian matrix of the transformation between the parameters of the network and the parameters of the observable variables. We compute the dimensions of several networks including the naive Bayes model with a hidden root node. 1
Optimization by learning and simulation of Bayesian and Gaussian networks
, 1999
"... Estimation of Distribution Algorithms (EDA) constitute an example of stochastics heuristics based on populations of individuals every of which encode the possible solutions to the optimization problem. These populations of individuals evolve in succesive generations as the search progresses  organ ..."
Abstract

Cited by 43 (6 self)
 Add to MetaCart
Estimation of Distribution Algorithms (EDA) constitute an example of stochastics heuristics based on populations of individuals every of which encode the possible solutions to the optimization problem. These populations of individuals evolve in succesive generations as the search progresses  organized in the same way as most evolutionary computation heuristics. In opposition to most evolutionary computation paradigms which consider the crossing and mutation operators as essential tools to generate new populations, EDA replaces those operators by the estimation and simulation of the joint probability distribution of the selected individuals. In this work, after making a review of the different approaches based on EDA for problems of combinatorial optimization as well as for problems of optimization in continuous domains, we propose new approaches based on the theory of probabilistic graphical models to solve problems in both domains. More precisely, we propose to adapt algorit...
A simple constraintbased algorithm for efficiently mining observational databases for causal relationships
 Data Mining and Knowledge Discovery
, 1997
"... Abstract. This paper presents a simple, efficient computerbased method for discovering causal relationships from databases that contain observational data. Observational data is passively observed, as contrasted with experimental data. Most of the databases available for data mining are observation ..."
Abstract

Cited by 28 (2 self)
 Add to MetaCart
Abstract. This paper presents a simple, efficient computerbased method for discovering causal relationships from databases that contain observational data. Observational data is passively observed, as contrasted with experimental data. Most of the databases available for data mining are observational. There is great potential for mining such databases to discover causal relationships. We illustrate how observational data can constrain the causal relationships among measured variables, sometimes to the point that we can conclude that one variable is causing another variable. The presentation here is based on a constraintbased approach to causal discovery. A primary purpose of this paper is to present the constraintbased causal discovery method in the simplest possible fashion in order to (1) readily convey the basic ideas that underlie more complex constraintbased causal discovery techniques, and (2) permit interested readers to rapidly program and apply the method to their own databases, as a start toward using more elaborate causal discovery algorithms.
A Scoring Function for Learning Bayesian Networks based on Mutual Information and Conditional Independence Tests
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2006
"... We propose a new scoring function for learning Bayesian networks from data using score search algorithms. This is based on the concept of mutual information and exploits some wellknown properties of this measure in a novel way. Essentially, a statistical independence test based on the chisquare di ..."
Abstract

Cited by 17 (0 self)
 Add to MetaCart
We propose a new scoring function for learning Bayesian networks from data using score search algorithms. This is based on the concept of mutual information and exploits some wellknown properties of this measure in a novel way. Essentially, a statistical independence test based on the chisquare distribution, associated with the mutual information measure, together with a property of additive decomposition of this measure, are combined in order to measure the degree of interaction between each variable and its parent variables in the network. The result is a nonBayesian scoring function called MIT (mutual information tests) which belongs to the family of scores based on information theory. The MIT score also represents a penalization of the KullbackLeibler divergence between the joint probability distributions associated with a candidate network and with the available data set. Detailed results of a complete experimental evaluation of the proposed scoring function and its comparison with the wellknown K2, BDeu and BIC/MDL scores are also presented.
Searching for Bayesian Network Structures in the Space of Restricted Acyclic Aprtially Directed Graphs
 Journal of Artificial Intelligence Research
, 2003
"... Although many algorithms have been designed to construct Bayesian network structures using dierent approaches and principles, they all employ only two methods: those based on independence criteria, and those based on a scoring function and a search procedure (although some methods combine the two). ..."
Abstract

Cited by 15 (2 self)
 Add to MetaCart
Although many algorithms have been designed to construct Bayesian network structures using dierent approaches and principles, they all employ only two methods: those based on independence criteria, and those based on a scoring function and a search procedure (although some methods combine the two). Within the score+search paradigm, the dominant approach uses local search methods in the space of directed acyclic graphs (DAGs), where the usual choices for de ning the elementary modi cations (local changes) that can be applied are arc addition, arc deletion, and arc reversal. In this paper, we propose a new local search method that uses a dierent search space, and which takes account of the concept of equivalence between network structures: restricted acyclic partially directed graphs (RPDAGs). In this way, the number of dierent con gurations of the search space is reduced, thus improving eciency. Moreover, although the nal result must necessarily be a local optimum given the nature of the search method, the topology of the new search space, which avoids making early decisions about the directions of the arcs, may help to nd better local optima than those obtained by searching in the DAG space.
The Posterior Probability of Bayes Nets with Strong Dependences
 Soft Computing
, 1999
"... Stochastic independence is an idealized relationship located at one end of a continuum of values measuring degrees of dependence. Modeling real world systems, we are often not interested in the distinction between exact independence and any degree of dependence, but between weak ignorable and strong ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
Stochastic independence is an idealized relationship located at one end of a continuum of values measuring degrees of dependence. Modeling real world systems, we are often not interested in the distinction between exact independence and any degree of dependence, but between weak ignorable and strong substantial dependence. Good models map significant deviance from independence and neglect approximate independence or dependence weaker than a noise threshold. This intuition is applied to learning the structure of Bayes nets from data. We determine the conditional posterior probabilities of structures given that the degree of dependence at each of their nodes exceeds a critical noise level. Deviance from independence is measured by mutual information. Arc probabilities are determined by the amount of mutual information the neighbors contribute to a node, is greater than a critical minimum deviance from independence. A Ø 2 approximation for the probability density function of mutual info...
Knowing and reasoning in
 in College: Gender Related Patterns in Student’s Intellectual Development
, 1992
"... Modelling a decision support system for ..."