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15
Learning Bayesian Networks from Data: An InformationTheory Based Approach
"... This paper provides algorithms that use an informationtheoretic analysis to learn Bayesian network structures from data. Based on our threephase learning framework, we develop efficient algorithms that can effectively learn Bayesian networks, requiring only polynomial numbers of conditional indepe ..."
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Cited by 92 (5 self)
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This paper provides algorithms that use an informationtheoretic analysis to learn Bayesian network structures from data. Based on our threephase learning framework, we develop efficient algorithms that can effectively learn Bayesian networks, requiring only polynomial numbers of conditional independence (CI) tests in typical cases. We provide precise conditions that specify when these algorithms are guaranteed to be correct as well as empirical evidence (from real world applications and simulation tests) that demonstrates that these systems work efficiently and reliably in practice.
An Algorithm for Bayesian Belief Network Construction from Data
 IN PROCEEDINGS OF AI & STATâ€™97
, 1997
"... This paper presents an efficient algorithm for constructing Bayesian belief networks from databases. The algorithm takes a database and an attributes ordering (i.e., the causal attributes of an attribute should appear earlier in the order) as input and constructs a belief network structure as output ..."
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Cited by 43 (6 self)
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This paper presents an efficient algorithm for constructing Bayesian belief networks from databases. The algorithm takes a database and an attributes ordering (i.e., the causal attributes of an attribute should appear earlier in the order) as input and constructs a belief network structure as output. The construction process is based on the computation of mutual information of attribute pairs. Given a data set which is large enough and has a DAGIsomorphic probability distribution, this algorithm guarantees that the perfect map [1] of the underlying dependency model is generated, and at the same time, enjoys the time complexity of O N ( ) on conditional independence (CI) tests. To evaluate this algorithm, we present the experimental results on three versions of the wellknown ALARM network database, which has 37 attributes and 10,000 records. The correctness proof and the analysis of computational complexity are also presented. We also discuss the features of our work and relate it to previous works.
Learning Bayesian Networks from Data: An Efficient Approach Based on Information Theory
, 1997
"... This paper addresses the problem of learning Bayesian network structures from data by using an information theoretic dependency analysis approach. Based on our threephase construction mechanism, two efficient algorithms have been developed. One of our algorithms deals with a special case where the ..."
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Cited by 35 (0 self)
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This paper addresses the problem of learning Bayesian network structures from data by using an information theoretic dependency analysis approach. Based on our threephase construction mechanism, two efficient algorithms have been developed. One of our algorithms deals with a special case where the node ordering is given, the algorithm only require ) ( 2 N O CI tests and is correct given that the underlying model is DAGFaithful [Spirtes et. al., 1996]. The other algorithm deals with the general case and requires ) ( 4 N O conditional independence (CI) tests. It is correct given that the underlying model is monotone DAGFaithful (see Section 4.4). A system based on these algorithms has been developed and distributed through the Internet. The empirical results show that our approach is efficient and reliable. 1 Introduction The Bayesian network is a powerful knowledge representation and reasoning tool under conditions of uncertainty. A Bayesian network is a directed acyclic graph ...
Constructing the Dependency Structure of a Multiagent Probabilistic Network
 IEEE Transactions on Knowledge and Data Engineering
, 2001
"... this paper, we propose an automated process for constructing the combined dependency structure of a ########## probabilistic network. Each domain expert supplies any known conditional independency information and not necessarily an explicit dependency structure. Our method determines a succinct r ..."
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Cited by 26 (16 self)
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this paper, we propose an automated process for constructing the combined dependency structure of a ########## probabilistic network. Each domain expert supplies any known conditional independency information and not necessarily an explicit dependency structure. Our method determines a succinct representation of all the supplied independency information called a ####### #####. This process involves detecting all ############ information and removing all ######### information. A ###### dependency structure of the multiagent probabilistic network can be constructed directly from this minimal cover. The main result of this paper is that the constructed dependency structure is a ########### of the minimal cover. That is, every probabilistic conditional independency logically implied by the minimal cover can be inferred from the dependency structure and every probabilistic conditional independency inferred from the dependency structure is logically implied by the minimal cover
A `Microscopic' Study of Minimum Entropy Search in Learning Decomposable Markov Networks
 MACHINE LEARNING
, 1995
"... Several scoring metrics are used in different search procedures for learning probabilistic networks. We study the properties of cross entropy in learning a decomposable Markov network. Though entropy and related scoring metrics were widely used, its `microscopic' properties and asymptotic behavior i ..."
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Cited by 23 (18 self)
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Several scoring metrics are used in different search procedures for learning probabilistic networks. We study the properties of cross entropy in learning a decomposable Markov network. Though entropy and related scoring metrics were widely used, its `microscopic' properties and asymptotic behavior in a search have not been analyzed. We present such a `microscopic' study of a minimum entropy search algorithm, and show that it learns an Imap of the domain model when the data size is large. Search procedures that modify a network structure one link at a time have been commonly used for efficiency. Our study indicates that a class of domain models cannot be learned by such procedures. This suggests that prior knowledge about the problem domain together with a multilink search strategy would provide an effective way to uncover many domain models.
A Bayesian Approach to User Profiling In Information Retrieval
 TECHNOLOGY LETTERS
, 2000
"... Numerous probability models have been suggested for information retrieval (IR) over the years. These models have been applied to try to manage the inherent uncertainty in IR, for instance, document and query representation, relevance feedback, and evaluating the effectiveness of IR system. On ..."
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Cited by 9 (2 self)
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Numerous probability models have been suggested for information retrieval (IR) over the years. These models have been applied to try to manage the inherent uncertainty in IR, for instance, document and query representation, relevance feedback, and evaluating the effectiveness of IR system. On the other hand, Bayesian networks have become an established probabilistic framework for uncertainty management in artificial intelligence. In this
Learning PseudoIndependent Models: Analytical and Experimental Results
 Advances in Artificial Intelligence
, 2000
"... . Most algorithms to learn belief networks use singlelink lookahead search to be efficient. It has been shown that such search procedures are problematic when applied to learning pseudoindependent (PI) models. Furthermore, some researchers have questioned whether PI models exist in practice. ..."
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Cited by 9 (5 self)
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. Most algorithms to learn belief networks use singlelink lookahead search to be efficient. It has been shown that such search procedures are problematic when applied to learning pseudoindependent (PI) models. Furthermore, some researchers have questioned whether PI models exist in practice. We present two nontrivial PI models which derive from a social study dataset. For one of them, the learned PI model reached ultimate prediction accuracy achievable given the data only, while using slightly more inference time than the learned nonPI model. These models provide evidence that PI models are not simply mathematical constructs. To develop efficient algorithms to learn PI models effectively we benefit from studying and understanding such models in depth. We further analyze how multiple PI submodels may interact in a larger domain model. Using this result, we show that the RML algorithm for learning PI models can learn more complex PI models than previously known. Keywor...
Automated Database Schema Design Using Mined Data Dependencies
 J. Amer. Soc. Inform. Sci
, 1998
"... Data dependencies are used in database schema design to enforce the correctness of a database as well as to reduce redundant data. These dependencies are usually determined from the semantics of the attributes and are then enforced upon the relations. This paper describes a bottomup procedure for d ..."
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Cited by 6 (0 self)
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Data dependencies are used in database schema design to enforce the correctness of a database as well as to reduce redundant data. These dependencies are usually determined from the semantics of the attributes and are then enforced upon the relations. This paper describes a bottomup procedure for discovering multivalued dependencies (MVDs) in observed data without knowing `a priori the relationships amongst the attributes. The proposed algorithm is an application of the technique we designed for learning conditional independencies in probabilistic reasoning. A prototype system for automated database schema design has been implemented. Experiments were carried out to demonstrate both the effectiveness and efficiency of our method. 1
Learning Conditional Independence Relations from a Probabilistic Model
, 1994
"... We consider the problem of learning conditional independencies, expressed as a Markov network, from a probabilistic model. An efficient algorithm employing a greedy search has been developed earlier with promising empirical results. However, two issues were not addressed. First, the reason why the m ..."
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Cited by 5 (0 self)
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We consider the problem of learning conditional independencies, expressed as a Markov network, from a probabilistic model. An efficient algorithm employing a greedy search has been developed earlier with promising empirical results. However, two issues were not addressed. First, the reason why the myopic search works so well globally has not been fully understood. Second, whether the algorithm can find a correct Markov network in all cases has not been formally established. In this paper, we prove that, for any given probabilistic model, the algorithm will always produce a Markov network whose structure is an independence map of the underlying model and whose associated probability distribution is identical to the underlying model. The proof also offers deeper insight into the algorithm's working mechanism. As the problem of learning a minimal independence map of a given probabilistic model is NPhard in general, our polynomial time algorithm does not guarantee minimality in all cases....
A Characterization of SingleLink Search in Learning Belief Networks
 Proc. Pacific Rim Knowledge Acquisition Workshop
, 1998
"... . One alternative to manual acquisition of belief networks from domain experts is automatic learning of these networks from data. Common algorithms for learning belief networks employ a singlelink lookahead search. It is unclear, however, what types of domain models are learnable by such algorithms ..."
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Cited by 4 (4 self)
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. One alternative to manual acquisition of belief networks from domain experts is automatic learning of these networks from data. Common algorithms for learning belief networks employ a singlelink lookahead search. It is unclear, however, what types of domain models are learnable by such algorithms and what types of models will escape. We conjecture that these learning algorithms that use a singlelink search are specializations of a simple algorithm which we call LIM. We put forward arguments that support such a conjecture, and then provide an axiomatic characterization of models learnable by LIM. The characterization coupled with the conjecture identifies models that are definitely learnable and definitely unlearnable by a class of learning algorithms. It also identifies models that are highly likely to escape these algorithms. Research to formally prove the conjecture is ongoing. Keywords: knowledge acquisition, learning, knowledge discovery. 1 Introduction Belief networks [9, 5...