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Bayesian Network Structure Learning by Recursive Autonomy Identification Raanan Yehezkel ∗ Video Analytics Group
"... We propose the recursive autonomy identification (RAI) algorithm for constraintbased (CB) Bayesian network structure learning. The RAI algorithm learns the structure by sequential application of conditional independence (CI) tests, edge direction and structure decomposition into autonomous substru ..."
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We propose the recursive autonomy identification (RAI) algorithm for constraintbased (CB) Bayesian network structure learning. The RAI algorithm learns the structure by sequential application of conditional independence (CI) tests, edge direction and structure decomposition into autonomous substructures. The sequence of operations is performed recursively for each autonomous substructure while simultaneously increasing the order of the CI test. While other CB algorithms dseparate structures and then direct the resulted undirected graph, the RAI algorithm combines the two processes from the outset and along the procedure. By this means and due to structure decomposition, learning a structure using RAI requires a smaller number of CI tests of high orders. This reduces the complexity and runtime of the algorithm and increases the accuracy by diminishing the curseofdimensionality. When the RAI algorithm learned structures from databases representing synthetic problems, known networks and natural problems, it demonstrated superiority with respect to computational complexity, runtime, structural correctness and classification accuracy over the
Efficient Markov Network Discovery Using Particle Filters
"... In this paper we introduce an efficient independencebased algorithm for the induction of the Markov network structure of a domain from the outcomes of independence test conducted on data. Our algorithm utilizes a particle filter (sequential Monte Carlo) method to maintain a population of Markov net ..."
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In this paper we introduce an efficient independencebased algorithm for the induction of the Markov network structure of a domain from the outcomes of independence test conducted on data. Our algorithm utilizes a particle filter (sequential Monte Carlo) method to maintain a population of Markov network structures that represent the posterior probability distribution over structures, given the outcomes of the tests performed. This enables us to select, at each step, the maximally informative test to conduct next from a pool of candidates according to information gain, which minimizes the cost of the statistical tests conducted on data. This makes our approach useful in domains where independence tests are expensive, such as cases of very large data sets and/or distributed data. In addition, our method maintains multiple candidate structures weighed by posterior probability, which allows flexibility in the presence of potential errors in the test outcomes.
A New Hybrid Method for Bayesian Network Learning With Dependency Constraints
"... Abstract — A Bayes net has qualitative and quantitative aspects: The qualitative aspect is its graphical structure that corresponds to correlations among the variables in the Bayes net. The quantitative aspects are the net parameters. This paper develops a hybrid criterion for learning Bayes net str ..."
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Abstract — A Bayes net has qualitative and quantitative aspects: The qualitative aspect is its graphical structure that corresponds to correlations among the variables in the Bayes net. The quantitative aspects are the net parameters. This paper develops a hybrid criterion for learning Bayes net structures that is based on both aspects. We combine model selection criteria measuring data fit with correlation information from statistical tests: Given a sample d, search for a structure G that maximizes score(G, d), over the set of structures G that satisfy the dependencies detected in d. We rely on the statistical test only to accept conditional dependencies, not conditional independencies. We show how to adapt local search algorithms to accommodate the observed dependencies. Simulation studies with GES search and the BDeu/BIC scores provide evidence that the additional dependency information leads to Bayes nets that better fit the target model in distribution and structure. I.
Spatiotemporal Models for DataAnomaly Detection in Dynamic Environmental Monitoring Campaigns
"... The ecological sciences have benefited greatly from recent advances in wireless sensor technologies. These technologies allow researchers to deploy networks of automated sensors, which can monitor a landscape at very fine temporal and spatial scales. However, these networks are subject to harsh cond ..."
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The ecological sciences have benefited greatly from recent advances in wireless sensor technologies. These technologies allow researchers to deploy networks of automated sensors, which can monitor a landscape at very fine temporal and spatial scales. However, these networks are subject to harsh conditions, which lead to malfunctions in individual sensors and failures in network communications. The resulting data streams often exhibit incorrect data measurements and missing values. Identifying and correcting these is timeconsuming and errorprone. We present a method for realtime automated data quality control (QC) that exploits the spatial and temporal correlations in the data to distinguish sensor failures from valid observations. The model adapts to each deployment site by learning a Bayesian network structure that captures spatial relationships between sensors, and it extends the structure to a dynamic Bayesian network to incorporate temporal correlations. This model is able to flag faulty observations and predict the true values of the missing or corrupt readings. The performance of the model is evaluated on data collected by the SensorScope Project. The results show that the spatiotemporal model demonstrates clear advantages over models that include only temporal or only spatial correlations, and that the model is capable of accurately imputing corrupted values. Categories and Subject Descriptors: I.2.6 [Artificial Intelligence]: Learning—Parameter learning; I.5.1 [Pattern Recognition]: Models—Statistical; structural; G.3 [Mathematics of Computing]: Probability and Statistics—Distribution functions; Markov processes; multivariate statistics
Penalized Likelihood Methods for Estimation of sparse high dimensional directed acyclic graphs
, 2010
"... Directed acyclic graphs are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges between nodes represent the influence of components of the system o ..."
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Directed acyclic graphs are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges between nodes represent the influence of components of the system on each other. Estimation of directed graphs from observational data is computationally NPhard. In addition, directed graphs with the same structure may be indistinguishable based on observations alone. When the nodes exhibit a natural ordering, the problem of estimating directed graphs reduces to the problem of estimating the structure of the network. In this paper, we propose an efficient penalized likelihood method for estimation of the adjacency matrix of directed acyclic graphs, when variables inherit a natural ordering. We study variable selection consistency of both the lasso, as well as the adaptive lasso penalties in high dimensional sparse settings, and propose an errorbased choice for selecting the tuning parameter. We show that although the lasso is only variable selection consistent under stringent conditions, the adaptive lasso can consistently estimate the true graph under the usual regularity assumptions. Simulation studies indicate that the correct ordering of the variables becomes less critical in estimation of high dimensional sparse networks.
Improved search for structure learning of large bayesian networks
"... The problem of Bayesian network structure learning is defined as an optimization problem over the space of all possible network structures. For lowdimensional data, optimal structure learning approaches exist. For highdimensional data, structure learning remains a significant challenge. Most commo ..."
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The problem of Bayesian network structure learning is defined as an optimization problem over the space of all possible network structures. For lowdimensional data, optimal structure learning approaches exist. For highdimensional data, structure learning remains a significant challenge. Most commonly, approaches to highdimensional structure learning employ a reduced search space and apply hill climbing methods to find highscoring network structures. But even the reduced search space contains many local optima so that local search methods are unable to find nearoptimal network structures. Instead of focusing on search space reduction, as most of the previous work in this area, we propose to replace the greedy search schemes with more effective search methods. We show that for highdimensional data the proposed search method finds significantly better structures than other leading approaches to structure learning. 1
A Statistical Implicative Analysis Based Algorithm and MMPC Algorithm for Detecting Multiple Dependencies
"... Discovering the dependencies among the variables of a domain from examples is an important problem in optimization. Many methods have been proposed for this purpose, but few largescale evaluations were conducted. Most of these methods are based on measurements of conditional probability. The statis ..."
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Discovering the dependencies among the variables of a domain from examples is an important problem in optimization. Many methods have been proposed for this purpose, but few largescale evaluations were conducted. Most of these methods are based on measurements of conditional probability. The statistical implicative analysis offers another perspective of dependencies. It is important to compare the results obtained using this approach with one of the best methods currently available for this task: the MMPC heuristic. As the SIA is not used directly to address this problem, we designed an extension of it for our purpose. We conducted a large number of experiments by varying parameters such as the number of dependencies, the number of variables involved or the type of their distribution to compare the two approaches. The results show strong complementarities of the two methods. Keywords: Statistical Implicative Analysis, multiple dependencies, Bayesian network.
Improving HighDimensional Bayesian Network Structure Learning by Exploiting Search Space Information
, 2006
"... Bayesian networks are frequently used to model statistical dependencies in data. Without prior knowledge of dependencies in the data, the structure of a Bayesian network is learned from the data. Bayesian network structure learning is commonly posed as an optimization problem where search is used to ..."
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Bayesian networks are frequently used to model statistical dependencies in data. Without prior knowledge of dependencies in the data, the structure of a Bayesian network is learned from the data. Bayesian network structure learning is commonly posed as an optimization problem where search is used to find structures that maximize a scoring function. Since the structure search space is superexponential in the number of variables in a network, heuristics are applied to constrain the search space of highdimensional networks. Greedy hill climbing is then applied in the reduced search space. The constrained search space of highdimensional networks contains many local maxima that greedy hill climbing cannot overcome. This issue has only been addressed by augmenting greedy search with TABU lists or random moves. This is not a holistic solution to the problem. By using a search algorithm that is global in nature, we are not confined to results in a particular region of the search space, like previous approaches. We present ModelBased Search (MBS) [1] applied to Bayesian network structure learning. MBS uses information gained during search to explore promising search space regions. Maintaining this search space information keeps a global view of the search task and helps find structures at higher maxima than greedy hill climbing. We show that MBS performs better than hill climbing in the MaxMin Parents and Children (MMPC) [30] search space and can find better highdimensional network structures than other leading structure learning algorithms. 1
Constraint relaxation for learning the structure of Bayesian networks
, 2009
"... This paper introduces constraint relaxation, a new strategy for learning the structure of Bayesian networks. Constraint relaxation identifies and “relaxes ” possibly inaccurate independence constraints on the structure of the model. We describe a heuristic algorithm for constraint relaxation that co ..."
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This paper introduces constraint relaxation, a new strategy for learning the structure of Bayesian networks. Constraint relaxation identifies and “relaxes ” possibly inaccurate independence constraints on the structure of the model. We describe a heuristic algorithm for constraint relaxation that combines greedy search in the space of undirected skeletons with edge orientation based on the constraints. This approach produces significant improvements in the structural accuracy of the learned models compared to four wellknown structure learning algorithms in an empirical evaluation using data sampled from both realworld and randomly generated networks. 1