Learning Optimal Bayesian Networks: A Shortest Path Perspective

Yuan, Changhe; Malone, Brandon

doi:10.1613/jair.4039

Cited by 146 publications

(140 citation statements)

References 47 publications

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“…An interesting research direction for the future is to extend our methods to handle with the datasets in which each variable has more than two values (i.e., r > 2). It will also be interesting to explore how to adapt our verification techniques to BN learning algorithms that can find a globally optimal structure for all possible variable orderings [19,14]. One possible solution to adapt our insertion-based method to these algorithms is to design artificial variables that can construct unique BN structures [16].…”

Section: Resultsmentioning

confidence: 99%

Result Integrity Verification of Outsourced Bayesian Network Structure Learning

Liu

Wang

Yuan

2014

Proceedings of the 2014 SIAM International Conference on Data Mining

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There has been considerable recent interest in the datamining-as-a-service paradigm: the client that lacks computational resources outsources his/her data and data mining needs to a third-party service provider. One of the security issues of this outsourcing paradigm is how the client can verify that the service provider indeed has returned correct data mining results. In this paper, we focus on the problem of result verification of outsourced Bayesian network (BN) structure learning. We consider the untrusted service provider that intends to return wrong BN structures. We develop three efficient probabilistic verification approaches to catch the incorrect BN structure with high probability and cheap overhead. Our experimental results demonstrate that our verification methods can capture wrong BN structure effectively and efficiently.

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Section: Resultsmentioning

confidence: 99%

Result Integrity Verification of Outsourced Bayesian Network Structure Learning

Liu

Wang

Yuan

2014

Proceedings of the 2014 SIAM International Conference on Data Mining

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“…It is a simple algorithm that is used to determine the belief-network structure with maximum probability. The probability is calculated based on multivariate uniform distribution (posterior distribution) ( [9], [10], [11], and [12]). Multivariate uniform distribution is a special case of Dirichlet distribution.…”

Section: Introductionmentioning

confidence: 99%

Prior and posterior dirichlet distributions on bayesian networks (BNs)

Saputro¹,

Widyaningsih²,

Handayani³

et al. 2017

AIP Conference Proceedings

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Abstract. Bayesian Networks (BNs) is a graphical representation model of some random variables and the relationship between the random variables. It is used to determine the joint probability of some random variables based on the posterior probability of each random variable. The posterior probability is calculated based on the parameters of the prior distribution. Prior distribution used in BNs includes the Dirichlet distribution. It is a conjugate prior for the multinomial distribution. Graph of BNs (belief-network structure) is determined by maximizing the probability of each random variable. One of the algorithms used to maximize it is K2 algorithm. The present research seeks to re-derive the joint probability in the belief-network structure using Dirichlet distribution, and to determine K2 algorithm for the structure. The joint probability obtained is the product of each probability of BNs random variable. The probability shows the dependence of a random variable with the others (parents). Based on these views, K2 algorithm can be used and Probability derived from the structure is considered as the product of the probability of each random variable. The probability of each random variable is calculated with the formula The belief-network structure is found out by determining a set of parents (πi) probably from random variables. Determination of the parents is based on the maximum probability of any random variable through algorithms K2.

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“…In general terms, the problem is to find the structure that maximizes a given score function that depends on the data [1]. The research on this topic is very active, with numerous methods and papers [2,3,4,5,6,7,8,9,10]. The main characteristic tying together all these methods is the score function.…”

Section: Introductionmentioning

confidence: 99%

Min-BDeu and Max-BDeu Scores for Learning Bayesian Networks

Scanagatta

Campos

Zaffalon

2014

Probabilistic Graphical Models

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Abstract. This work presents two new score functions based on the Bayesian Dirichlet equivalent uniform (BDeu) score for learning Bayesian network structures. They consider the sensitivity of BDeu to varying parameters of the Dirichlet prior. The scores take on the most adversary and the most beneficial priors among those within a contamination set around the symmetric one. We build these scores in such way that they are decomposable and can be computed efficiently. Because of that, they can be integrated into any state-of-the-art structure learning method that explores the space of directed acyclic graphs and allows decomposable scores. Empirical results suggest that our scores outperform the standard BDeu score in terms of the likelihood of unseen data and in terms of edge discovery with respect to the true network, at least when the training sample size is small. We discuss the relation between these new scores and the accuracy of inferred models. Moreover, our new criteria can be used to identify the amount of data after which learning is saturated, that is, additional data are of little help to improve the resulting model.

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Learning Optimal Bayesian Networks: A Shortest Path Perspective

Cited by 146 publications

References 47 publications

Result Integrity Verification of Outsourced Bayesian Network Structure Learning

Result Integrity Verification of Outsourced Bayesian Network Structure Learning

Prior and posterior dirichlet distributions on bayesian networks (BNs)

Min-BDeu and Max-BDeu Scores for Learning Bayesian Networks

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