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12
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 ..."
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Cited by 43 (6 self)
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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...
On the Dirichlet Prior and Bayesian Regularization
 In Advances in Neural Information Processing Systems 15
, 2002
"... A common objective in learning a model from data is to recover its network structure, while the model parameters are of minor interest. For example, we may wish to recover regulatory networks from highthroughput data sources. In this paper we examine how Bayesian regularization using a Dirichle ..."
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Cited by 22 (2 self)
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A common objective in learning a model from data is to recover its network structure, while the model parameters are of minor interest. For example, we may wish to recover regulatory networks from highthroughput data sources. In this paper we examine how Bayesian regularization using a Dirichlet prior over the model parameters affects the learned model structure in a domain with discrete variables. Surprisingly, a weak prior in the sense of smaller equivalent sample size leads to a strong regularization of the model structure (sparse graph) given a sufficiently large data set. In particular, the empty graph is obtained in the limit of a vanishing strength of prior belief. This is diametrically opposite to what one may expect in this limit, namely the complete graph from an (unregularized) maximum likelihood estimate. Since the prior affects the parameters as expected, the prior strength balances a "tradeoff" between regularizing the parameters or the structure of the model. We demonstrate the benefits of optimizing this tradeoff in the sense of predictive accuracy.
Combinatorial optimization by learning and simulation of Bayesian networks
 in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence
, 2000
"... This paper shows how the Bayesian network paradigm can be used in order to solve combinatorial optimization problems. To do it some methods of structure learning from data and simulation of Bayesian networks are inserted inside Estimation of Distribution Algorithms (EDA). EDA are a new tool for evol ..."
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Cited by 22 (10 self)
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This paper shows how the Bayesian network paradigm can be used in order to solve combinatorial optimization problems. To do it some methods of structure learning from data and simulation of Bayesian networks are inserted inside Estimation of Distribution Algorithms (EDA). EDA are a new tool for evolutionary computation in which populations of individuals are created by estimation and simulation of the joint probability distribution of the selected individuals. We propose new approaches to EDA for combinatorial optimization based on the theory of probabilistic graphical models. Experimental results 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). ..."
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Cited by 15 (2 self)
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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.
Learning Bayes net structure from sparse data sets
, 2001
"... There are essentially two kinds of approaches for learning the structure of Bayesian Networks (BNs) from data. The first approach tries to find a graph which satis es all the constraints implied by the empirical conditional independencies measured in the data [PV91, SGS00a, Shi00]. The second approa ..."
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Cited by 14 (2 self)
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There are essentially two kinds of approaches for learning the structure of Bayesian Networks (BNs) from data. The first approach tries to find a graph which satis es all the constraints implied by the empirical conditional independencies measured in the data [PV91, SGS00a, Shi00]. The second approach searches through the space of models (either DAGs or PDAGs), and uses some scoring metric (typically Bayesian or some approximation, such as BIC/MDL) to evaluate the models [CH92, Hec95, Hec98, Kra98], typically returning the highest scoring model found. Our main interest is in learning BN structure from gene expression data [FLNP00, HGJY01, MM99, SGS00b]. In domains such as this, where the ratio of the number of observations to the number of variables is low (i.e., when we have sparse data), selecting a threshold for the conditional independence (CI) tests can be tricky, and repeated use of such tests can lead to inconsistencies [DD99]. Bayesian s...
Inexact graph matching by means of Estimation of Distribution Algorithms
"... Estimation of Distribution Algorithms (EDAs) are a quite recent topic in optimization techniques. They combine two technical disciplines of soft computing methodologies: probabilistic reasoning and evolutionary computing. Several algorithms and approaches have already been proposed by different auth ..."
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Cited by 12 (2 self)
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Estimation of Distribution Algorithms (EDAs) are a quite recent topic in optimization techniques. They combine two technical disciplines of soft computing methodologies: probabilistic reasoning and evolutionary computing. Several algorithms and approaches have already been proposed by different authors, but up to now there are very few papers showing their potential and comparing them to other evolutionary computational methods and algorithms such as Genetic Algorithms (GAs). This paper focuses on the problem of inexact graph matching which is NPhard and requires techniques to find an approximate acceptable solution. This problem arises when a non bijective correspondence is searched between two graphs. A typical instance of this problem corresponds to the case where graphs are used for structural pattern recognition in images. EDA algorithms are well suited for this type of problems.
Inexact graph matching using learning and simulation of Bayesian networks. An empirical comparison between different approaches with synthetic data
, 2000
"... Estimation Distribution Algorithms (EDAs) is a quite recent topic in optimisation techniques. Several algorithms and approaches have already been proposed by different authors, but up to now there are very few papers showing their potential and comparing them to other evolutionary computation method ..."
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Cited by 6 (1 self)
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Estimation Distribution Algorithms (EDAs) is a quite recent topic in optimisation techniques. Several algorithms and approaches have already been proposed by different authors, but up to now there are very few papers showing their potential and comparing them to other evolutionary computation methods and algorithms such as Genetic Algorithms (GAs). A problem such as inexact graph matching is NPhard and requires techniques that approximate to an acceptable solution. This problem arises when a non bijective correspondence is searched between two graphs G1 and G2 . A typical instance of this problem corresponds to the case where G1 is a model of the scene, and G2 is a graph derived from data (e.g. an image of the scene). EDA algorithms are well suited for this type of problems. This paper proposes to use EDA algorithms as a new approach for inexact graph matching. Also, two adaptations of the EDA approach to problems with constraints are described on the form of two techniques to cont...
BCourse: A Web Service for Bayesian Data Analysis
"... BCourse is a free webbased online data analysis tool, which allows the users to analyze their data for multivariate probabilistic dependencies. These dependencies are represented as Bayesian network models. In addition to this, BCourse also oers facilities for inferring certain type of causal ..."
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Cited by 3 (1 self)
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BCourse is a free webbased online data analysis tool, which allows the users to analyze their data for multivariate probabilistic dependencies. These dependencies are represented as Bayesian network models. In addition to this, BCourse also oers facilities for inferring certain type of causal dependencies from the data. The software uses a novel "tutorial style" userfriendly interface which intertwines the steps in the data analysis with support material that gives an informal introduction to the Bayesian approach adopted. Although the analysis methods, modeling assumptions and restrictions are totally transparent to the user, this transparency is not achieved at the expense of analysis power: with the restrictions stated in the support material, BCourse is a powerful analysis tool exploiting several theoretically elaborate results developed recently in the elds of Bayesian and causal modeling. BCourse can be used with most webbrowsers (even Lynx), and the facilities include features such as automatic missing data handling and discretization, a exible graphical interface for probabilistic inference on the constructed Bayesian network models (for Java enabled browsers), automatic prettyprinted layout for the networks, exportation of the models, and analysis of the importance of the derived dependencies. In this paper we discuss both the theoretical design principles underlying the BCourse tool, and the pragmatic methods adopted in the implementation of the software.
Advanced Fuzzy Clustering and Decision Tree PlugIns for DataEngine tm
"... Abstract. Although a large variety of data analysis tools are available on the market today, none of them is perfect; they all have their strengths and weaknesses. In such a situation it is important that a user can enhance the capabilities of a data analysis tool by his or her own favourite methods ..."
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Abstract. Although a large variety of data analysis tools are available on the market today, none of them is perfect; they all have their strengths and weaknesses. In such a situation it is important that a user can enhance the capabilities of a data analysis tool by his or her own favourite methods in order to compensate for shortcomings of the shipped version. However, only few commercial products offer such a possibility. A rare exception is DataEngine tm, which is provided with a welldocumented interface for userdefined function blocks (plugins). In this paper we describe three plugins we implemented for this wellknown tool: An advanced fuzzy clustering plugin that extends the fuzzy cmeans algorithm (which is a builtin feature of DataEngine tm) by other, more flexible algorithms, a decision tree classifier plugin that overcomes the serious drawback that DataEngine tm lacks a native module for this highly important technique, and finally a naive Bayes classifier plugin that makes available an old and timetested statistical classification method. 1
Bayesian Networks for Feature Subset Selection
, 2000
"... We present FSSEBNA, a new randomized, populationbased and evolutionary algorithm which deals with the well known FSS problem on Data Mining applications. In FSSEBNA, the FSS problem, stated as a search problem, uses the EBNA (Estimation of Bayesian Network Algorithm) search engine, an algorithm w ..."
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We present FSSEBNA, a new randomized, populationbased and evolutionary algorithm which deals with the well known FSS problem on Data Mining applications. In FSSEBNA, the FSS problem, stated as a search problem, uses the EBNA (Estimation of Bayesian Network Algorithm) search engine, an algorithm within the EDA (Estimation of Distribution Algorithm) approach. The EDA paradigm was born from the roots of the GA community in order to explicitly discover the relationships among the features of the problem and not disrupt them by genetic recombination operators. The EDA paradigm avoids the use of recombination operators and it guarantees the evolution of the population of solutions and the discovery of these relationships by the factorization of the probability distribution of best individuals in each generation of the search. In EBNA, this factorization is carried out by a Bayesian network induced by a cheap local search mechanism. Promising results on a set of real domains are achieved...