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49
On Recovery Algorithm for Chain Graphs
, 1997
"... The class of chain graphs (CGs) involving both undirected graphs (= Markov networks) and directed acyclic graphs (= Bayesian networks) was introduced in middle eighties for description of probabilistic conditional independence structures. Every class of Markov equivalent CGs (that is CGs describing ..."
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Cited by 10 (2 self)
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The class of chain graphs (CGs) involving both undirected graphs (= Markov networks) and directed acyclic graphs (= Bayesian networks) was introduced in middle eighties for description of probabilistic conditional independence structures. Every class of Markov equivalent CGs (that is CGs describing the same conditional independence structure) has a natural representative, which is called the largest CG. The paper presents socalled recovery algorithm, which on basis of the conditional independence structure given by a CG (in form of socalled dependency model) finds the largest CG, representing the corresponding class of Markov equivalent CGs. As a byproduct a graphical characterization of graphs, which are the largest CGs (for a class of Markov equivalent CGs) is obtained, and a simple algorithm changing every CG into the largest CG of the corresponding equivalence class is given. 1 INTRODUCTION Classic graphical approaches to description of probabilistic conditional independence stru...
Bayesian Network Classifiers in Weka
, 2004
"... Various Bayesian network classifier learning algorithms are implemented in Weka [10]. This note ..."
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Various Bayesian network classifier learning algorithms are implemented in Weka [10]. This note
Mind Change Optimal Learning of Bayes Net Structure". O.Schulte
 in Proceedings of the 20th Annual Conference on Learning Theory
, 2007
"... Abstract. This paper analyzes the problem of learning the structure of a Bayes net (BN) in the theoretical framework of Gold’s learning paradigm. Bayes nets are one of the most prominent formalisms for knowledge representation and probabilistic and causal reasoning. We follow constraintbased approa ..."
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Cited by 9 (2 self)
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Abstract. This paper analyzes the problem of learning the structure of a Bayes net (BN) in the theoretical framework of Gold’s learning paradigm. Bayes nets are one of the most prominent formalisms for knowledge representation and probabilistic and causal reasoning. We follow constraintbased approaches to learning Bayes net structure, where learning is based on observed conditional dependencies between variables of interest (e.g., “X is dependent on Y given any assignment to variable Z”). Applying learning criteria in this model leads to the following results. (1) The mind change complexity of identifying a Bayes net graph over variables V from dependency data is � � V, the maximum number of 2 edges. (2) There is a unique fastest mindchange optimal Bayes net learner; convergence speed is evaluated using Gold’s dominance notion of “uniformly faster convergence”. This learner conjectures a graph if it is the unique Bayes net pattern that satisfies the observed dependencies with a minimum number of edges, and outputs “no guess ” otherwise. Therefore we are using standard learning criteria to define a natural and novel Bayes net learning algorithm. We investigate the complexity of computing the output of the fastest mindchange optimal learner, and show that this problem is NPhard (assuming P=RP). To our knowledge this is the first NPhardness result concerning the existence of a uniquely optimal Bayes net structure. 1
On Separation Criterion and Recovery Algorithm for Chain Graphs
, 1996
"... Chain graphs (CGs) give a natural unifying point of view on Markov and Bayesian networks and enlarge the potential of graphical models for description of conditional independence structures. In the paper a direct graphical separation criterion for CGs which generalizes the dseparation criterion for ..."
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Cited by 7 (1 self)
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Chain graphs (CGs) give a natural unifying point of view on Markov and Bayesian networks and enlarge the potential of graphical models for description of conditional independence structures. In the paper a direct graphical separation criterion for CGs which generalizes the dseparation criterion for Bayesian networks is introduced (recalled) . It is equivalent to the classic moralization criterion for CGs and complete in the sense that for every CG there exists a probability distribution satisfying exactly independencies derivable from the CG by the separation criterion. Every class of Markov equivalent CGs can be uniquely described by a natural representative, called the largest CG. A recovery algorithm, which on basis of the (conditional) dependency model given by a CG finds the corresponding largest CG, is presented. 1 INTRODUCTION Traditional graphical models for description of probabilistic conditional independence structure use either undirected graphs (UGs), named also Markov n...
A geometric view on learning Bayesian network structures
, 2009
"... We recall the basic idea of an algebraic approach to learning Bayesian network (BN) structures, namely to represent every BN structure by a certain (uniquely determined) vector, called a standard imset. The main result of the paper is that the set of standard imsets is the set of vertices ( = extrem ..."
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Cited by 7 (3 self)
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We recall the basic idea of an algebraic approach to learning Bayesian network (BN) structures, namely to represent every BN structure by a certain (uniquely determined) vector, called a standard imset. The main result of the paper is that the set of standard imsets is the set of vertices ( = extreme points) of a certain polytope. Motivated by the geometric view, we introduce the concept of the geometric neighborhood for standard imsets, and, consequently, for BN structures. Then we show that it always includes the inclusion neighborhood, which was introduced earlier in connection with the greedy equivalence search (GES) algorithm. The third result is that the global optimum of an affine function over the polytope coincides with the local optimum relative to the geometric neighborhood. To illustrate the new concept by an example, we describe the geometric neighborhood in the case of three variables and show it differs from the inclusion neighborhood. This leads to a simple example of the failure of the GES algorithm if data are not “generated ” from a perfectly Markovian distribution. The point is that one can avoid this failure if the search technique is based on the geometric neighborhood instead. We also found out what is the geometric neighborhood in the case of four and five variables.
Finding Optimal Bayesian Network Given a SuperStructure
"... Classical approaches used to learn Bayesian network structure from data have disadvantages in terms of complexity and lower accuracy of their results. However, a recent empirical study has shown that a hybrid algorithm improves sensitively accuracy and speed: it learns a skeleton with an independenc ..."
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Classical approaches used to learn Bayesian network structure from data have disadvantages in terms of complexity and lower accuracy of their results. However, a recent empirical study has shown that a hybrid algorithm improves sensitively accuracy and speed: it learns a skeleton with an independency test (IT) approach and constrains on the directed acyclic graphs (DAG) considered during the searchandscore phase. Subsequently, we theorize the structural constraint by introducing the concept of superstructure S, which is an undirected graph that restricts the search to networks whose skeleton is a subgraph of S. We develop a superstructure constrained optimal search (COS): its time complexity is upper bounded by O(γm n), where γm < 2 depends on the maximal degree m of S. Empirically, complexity depends on the average degree ˜m and sparse structures allow larger graphs to be calculated. Our algorithm is faster than an optimal search by several orders and even finds more accurate results when given a sound superstructure. Practically, S can be approximated by IT approaches; significance level of the tests controls its sparseness, enabling to control the tradeoff between speed and accuracy. For incomplete superstructures, a greedily postprocessed version (COS+) still enables to significantly outperform other heuristic searches. Keywords: subset Bayesian networks, structure learning, optimal search, superstructure, connected 1.
Local search methods for learning Bayesian networks using a modified neighborhood in the space of dags
 Lecture Notes in Computer Science
, 2002
"... Abstract. The dominant approach for learning Bayesian networks from data is based on the use ofa scoring metric, that evaluates the fitness of any given candidate network to the data, and a search procedure, that explores the space ofpossible solutions. The most efficient methods used in this contex ..."
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Cited by 6 (4 self)
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Abstract. The dominant approach for learning Bayesian networks from data is based on the use ofa scoring metric, that evaluates the fitness of any given candidate network to the data, and a search procedure, that explores the space ofpossible solutions. The most efficient methods used in this context are (Iterated) Local Search algorithms. These methods use a predefined neighborhood structure that defines the feasible elementary modifications (local changes) that can be applied to a given solution in order to get another, potentially better solution. Ifthe search space is the set ofdirected acyclic graphs (dags), the usual choices for local changes are arc addition, arc deletion and arc reversal. In this paper we propose a new definition ofneighborhood in the dag space, which uses a modified operator for arc reversal. The motivation for this new operator is the observation that local search algorithms experience problems when some arcs are wrongly oriented. We exemplify the general usefulness of our proposal by means ofa set ofexperiments with different metrics and different local search methods, including HillClimbing and Greedy Randomized Adaptive Search Procedure (GRASP), as well as using several domain problems. 1
Efficient Learning using Constrained Sufficient Statistics
 Proceedings of the 7th International Workshop on Artificial Intelligence and Statistic
, 1999
"... Learning Bayesian networks is a central problem for pattern recognition, density estimation and classification. In this paper, we propose a new method for speeding up the computational process of learning Bayesian network structure. This approach uses constraints imposed by the statistics already co ..."
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Cited by 5 (0 self)
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Learning Bayesian networks is a central problem for pattern recognition, density estimation and classification. In this paper, we propose a new method for speeding up the computational process of learning Bayesian network structure. This approach uses constraints imposed by the statistics already collected from the data to guide the learning algorithm. This allows us to reduce the number of statistics collected during learning and thus speed up the learning time. We show that our method is capable of learning structure from data more efficiently than traditional approaches. Our technique is of particular importance when the size of the datasets is large or when learning from incomplete data. The basic technique that we introduce is general and can be used to improve learning performance in many settings where sufficient statistics must be computed. In addition, our technique may be useful for alternate search strategies such as branch and bound algorithms. 1 Introduction In recent yea...
A reconstruction algorithm for the essential graph
, 2008
"... A standard graphical representative of a Bayesian network structure is a special chain graph, known as an essential graph. An alternative algebraic approach to the mathematical description of this statistical model uses instead a certain integervalued vector, known as a standard imset. We give a di ..."
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Cited by 5 (2 self)
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A standard graphical representative of a Bayesian network structure is a special chain graph, known as an essential graph. An alternative algebraic approach to the mathematical description of this statistical model uses instead a certain integervalued vector, known as a standard imset. We give a direct formula for the translation of any chain graph describing a Bayesian network structure into the standard imset. Moreover, we present a twostage algorithm which makes it possible to reconstruct the essential graph on the basis of the standard imset. The core of this paper is the proof of the correctness of the algorithm.
Combining Multiple Perspectives
 In Proceedings of the Seventeenth International Conference on Machine Learning
, 2000
"... We consider a group of Bayesian learners whose interactions with the environment and other agents allow them to improve their model of the dependency among various factors that have influence on their interactions with the environment. Effective collaboration can improve the performance of isolated ..."
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Cited by 3 (3 self)
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We consider a group of Bayesian learners whose interactions with the environment and other agents allow them to improve their model of the dependency among various factors that have influence on their interactions with the environment. Effective collaboration can improve the performance of isolated individual learners. We present a mechanism to pool together the knowledge of many modelers in the domain, each of whom may have only partial access to the environment. The application domain used in this study is a multiagent negotiation problem. We present results to compare the performance of such knowledgecomposition against isolated learners, as also against a learner who has complete access to the environment.