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19
Construction of Bayesian Network Structures From Data: A Brief Survey and an Efficient Algorithm
, 1995
"... Previous algorithms for the recovery of Bayesian belief network structures from data have been either highly dependent on conditional independence (CI) tests, or have required on ordering on the nodes to be supplied by the user. We present an algorithm that integrates these two approaches: CI tests ..."
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Cited by 77 (8 self)
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Previous algorithms for the recovery of Bayesian belief network structures from data have been either highly dependent on conditional independence (CI) tests, or have required on ordering on the nodes to be supplied by the user. We present an algorithm that integrates these two approaches: CI tests are used to generate an ordering on the nodes from the database, which is then used to recover the underlying Bayesian network structure using a nonCltestbased method. Results of the evaluation of the algorithm on a number of databases (e.g., ALARM, LED, and SOYBEAN) are presented. We also discuss some algorithm performance issues and open problems.
Efficient Learning of Selective Bayesian Network Classifiers
, 1995
"... In this paper, we present a computationally efficient method for inducing selective Bayesian network classifiers. Our approach is to use informationtheoretic metrics to efficiently select a subset of attributes from which to learn the classifier. We explore three conditional, informationtheoretic ..."
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Cited by 50 (4 self)
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In this paper, we present a computationally efficient method for inducing selective Bayesian network classifiers. Our approach is to use informationtheoretic metrics to efficiently select a subset of attributes from which to learn the classifier. We explore three conditional, informationtheoretic metrics that are extensions of metrics used extensively in decision tree learning, namely Quinlan's gain and gain ratio metrics and Mantaras's distance metric. We experimentally show that the algorithms based on gain ratio and distance metric learn selective Bayesian networks that have predictive accuracies as good as or better than those learned by existing selective Bayesian network induction approaches (K2AS), but at a significantly lower computational cost. We prove that the subsetselection phase of these informationbased algorithms has polynomial complexity as compared to the worstcase exponential time complexity of the corresponding phase in K2AS. We also compare the performance o...
Improved learning of Bayesian networks
 Proc. of the Conf. on Uncertainty in Artificial Intelligence
, 2001
"... Two or more Bayesian network structures are Markov equivalent when the corresponding acyclic digraphs encode the same set of conditional independencies. Therefore, the search space of Bayesian network structures may be organized in equivalence classes, where each of them represents a different set o ..."
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Cited by 37 (6 self)
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Two or more Bayesian network structures are Markov equivalent when the corresponding acyclic digraphs encode the same set of conditional independencies. Therefore, the search space of Bayesian network structures may be organized in equivalence classes, where each of them represents a different set of conditional independencies. The collection of sets of conditional independencies obeys a partial order, the socalled “inclusion order.” This paper discusses in depth the role that the inclusion order plays in learning the structure of Bayesian networks. In particular, this role involves the way a learning algorithm traverses the search space. We introduce a condition for traversal operators, the inclusion boundary condition, which, when it is satisfied, guarantees that the search strategy can avoid local maxima. This is proved under the assumptions that the data is sampled from a probability distribution which is faithful to an acyclic digraph, and the length of the sample is unbounded. The previous discussion leads to the design of a new traversal operator and two new learning algorithms in the context of heuristic search and the Markov Chain Monte Carlo method. We carry out a set of experiments with synthetic and realworld data that show empirically the benefit of striving for the inclusion order when learning Bayesian networks from data.
Learning Probabilistic Networks
 THE KNOWLEDGE ENGINEERING REVIEW
, 1998
"... A probabilistic network is a graphical model that encodes probabilistic relationships between variables of interest. Such a model records qualitative influences between variables in addition to the numerical parameters of the probability distribution. As such it provides an ideal form for combini ..."
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Cited by 36 (1 self)
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A probabilistic network is a graphical model that encodes probabilistic relationships between variables of interest. Such a model records qualitative influences between variables in addition to the numerical parameters of the probability distribution. As such it provides an ideal form for combining prior knowledge, which might be limited solely to experience of the influences between some of the variables of interest, and data. In this paper, we first show how data can be used to revise initial estimates of the parameters of a model. We then progress to showing how the structure of the model can be revised as data is obtained. Techniques for learning with incomplete data are also covered.
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 ..."
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Cited by 28 (2 self)
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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.
Probabilistic Network Construction Using the Minimum Description Length Principle
, 1994
"... Probabilistic networks can be constructed from a database of cases by selecting a network that has highest quality with respect to this database according to a given measure. A new measure is presented for this purpose based on a minimum description length (MDL) approach. This measure is compared wi ..."
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Cited by 28 (1 self)
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Probabilistic networks can be constructed from a database of cases by selecting a network that has highest quality with respect to this database according to a given measure. A new measure is presented for this purpose based on a minimum description length (MDL) approach. This measure is compared with a commonly used measure based on a Bayesian approach both from a theoretical and an experimental point of view. We show that the two measures have the same properties for infinite large databases. For smaller databases, however, the MDL measure assigns equal quality to networks that represent the same set of independencies while the Bayesian measure does not. Preliminary test results suggest that an algorithm for learning probabilistic networks using the minimum description length approach performs comparably to a learning algorithm using the Bayesian approach. However, the former is slightly faster.
Learning Bayesian Networks Using Feature Selection
 in D. Fisher & H. Lenz, eds, Proceedings of the fifth International Workshop on Artificial Intelligence and Statistics, Ft. Lauderdale, FL
, 1995
"... This paper introduces a novel enhancement for learning Bayesian networks with a bias for small, highpredictiveaccuracy networks. The new approach selects a subset of features which maximizes predictive accuracy prior to the network learning phase. We examine explicitly the effects of two aspects o ..."
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Cited by 19 (2 self)
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This paper introduces a novel enhancement for learning Bayesian networks with a bias for small, highpredictiveaccuracy networks. The new approach selects a subset of features which maximizes predictive accuracy prior to the network learning phase. We examine explicitly the effects of two aspects of the algorithm, feature selection and node ordering. Our approach generates networks which are computationally simpler to evaluate and which display predictive accuracy comparable to that of Bayesian networks which model all attributes. 1 INTRODUCTION Bayesian networks are being increasingly recognized as an important representation for probabilistic reasoning. For many domains, the need to specify the probability distributions for a Bayesian network is considerable, and learning these probabilities from data using an algorithm like K2 [8] 1 could alleviate such specification difficulties. We describe an extension to the Bayesian network learning approaches introduced in K2. Rather than ...
On Local Optima in Learning Bayesian Networks
, 2003
"... This paper proposes and evaluates the kgreedy equivalence search algorithm (KES) for learning Bayesian networks (BNs) from complete data. The main characteristic of KES is that it allows a tradeoff between greediness and randomness, thus exploring different good local optima when run repeatedly. W ..."
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Cited by 17 (4 self)
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This paper proposes and evaluates the kgreedy equivalence search algorithm (KES) for learning Bayesian networks (BNs) from complete data. The main characteristic of KES is that it allows a tradeoff between greediness and randomness, thus exploring different good local optima when run repeatedly. When
A method for learning belief networks that contain hidden variables
 in Proceedings of the Workshop on Knowledge Discovery in Databases
, 1994
"... This paper presents a Bayesian method for computing the probability of a Bayesian beliefnetwork structure from a database. In particular, the paper focuses on computing the probability of a beliefnetwork structure that contains e. hidden (latent) variable. A hidden variable represents a postulated ..."
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Cited by 10 (4 self)
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This paper presents a Bayesian method for computing the probability of a Bayesian beliefnetwork structure from a database. In particular, the paper focuses on computing the probability of a beliefnetwork structure that contains e. hidden (latent) variable. A hidden variable represents a postulated entity about which we have no data. For example, we may wish to postulate the existence of a hidden
Courses of Action Development and Evaluation
 Proceedings for the 1998 Command and Control Research and Technology Symposium, Naval Postgraduate School
, 1998
"... This paper describes a set of procedures that will enhance the analysis, synthesis, and execution of courses of action (COA). The paper presents a set of formal methods for extending the capability of probabilistic models (influence nets) to produce rigorous mathematical models that reveal the impac ..."
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Cited by 7 (2 self)
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This paper describes a set of procedures that will enhance the analysis, synthesis, and execution of courses of action (COA). The paper presents a set of formal methods for extending the capability of probabilistic models (influence nets) to produce rigorous mathematical models that reveal the impact of the sequence and timing of actionable events on the outcome and effects desired in a situation. By incorporating timing information, such a model can be converted to a Discrete Event System (DES) model in the form of a Colored Petri Net. The DES model, when run as a simulation, can reveal the changes in the likelihood of the desired effects over time for any timed sequence of actionable events that comprise a COA. The paper presents DES analysis techniques that can generate all of the possible sequences of probability values of the outcome given any COA without simulation. Procedures are presented to select desirable sequences from the set of all sequences and determine the temporal relationship among the actionable events that will generate a selected sequence of probability values. 1.