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79
Using Bayesian networks to analyze expression data
 Journal of Computational Biology
, 2000
"... DNA hybridization arrays simultaneously measure the expression level for thousands of genes. These measurements provide a “snapshot ” of transcription levels within the cell. A major challenge in computational biology is to uncover, from such measurements, gene/protein interactions and key biologica ..."
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Cited by 753 (16 self)
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DNA hybridization arrays simultaneously measure the expression level for thousands of genes. These measurements provide a “snapshot ” of transcription levels within the cell. A major challenge in computational biology is to uncover, from such measurements, gene/protein interactions and key biological features of cellular systems. In this paper, we propose a new framework for discovering interactions between genes based on multiple expression measurements. This framework builds on the use of Bayesian networks for representing statistical dependencies. A Bayesian network is a graphbased model of joint multivariate probability distributions that captures properties of conditional independence between variables. Such models are attractive for their ability to describe complex stochastic processes and because they provide a clear methodology for learning from (noisy) observations. We start by showing how Bayesian networks can describe interactions between genes. We then describe a method for recovering gene interactions from microarray data using tools for learning Bayesian networks. Finally, we demonstrate this method on the S. cerevisiae cellcycle measurements of Spellman et al. (1998). Key words: gene expression, microarrays, Bayesian methods. 1.
Estimating highdimensional directed acyclic graphs with the PCalgorithm
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2007
"... We consider the PCalgorithm (Spirtes et al., 2000) for estimating the skeleton and equivalence class of a very highdimensional directed acyclic graph (DAG) with corresponding Gaussian distribution. The PCalgorithm is computationally feasible and often very fast for sparse problems with many nodes ..."
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Cited by 48 (4 self)
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We consider the PCalgorithm (Spirtes et al., 2000) for estimating the skeleton and equivalence class of a very highdimensional directed acyclic graph (DAG) with corresponding Gaussian distribution. The PCalgorithm is computationally feasible and often very fast for sparse problems with many nodes (variables), and it has the attractive property to automatically achieve high computational efficiency as a function of sparseness of the true underlying DAG. We prove uniform consistency of the algorithm for very highdimensional, sparse DAGs where the number of nodes is allowed to quickly grow with sample size n, as fast as O(n a) for any 0 < a < ∞. The sparseness assumption is rather minimal requiring only that the neighborhoods in the DAG are of lower order than sample size n. We also demonstrate the PCalgorithm for simulated data.
Learning graphical model structure using L1regularization paths
 In Proceedings of the 21st Conference on Artificial Intelligence (AAAI
, 2007
"... Sparsitypromoting L1regularization has recently been succesfully used to learn the structure of undirected graphical models. In this paper, we apply this technique to learn the structure of directed graphical models. Specifically, we make three contributions. First, we show how the decomposability ..."
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Cited by 22 (1 self)
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Sparsitypromoting L1regularization has recently been succesfully used to learn the structure of undirected graphical models. In this paper, we apply this technique to learn the structure of directed graphical models. Specifically, we make three contributions. First, we show how the decomposability of the MDL score, plus the ability to quickly compute entire regularization paths, allows us to efficiently pick the optimal regularization parameter on a pernode basis. Second, we show how to use L1 variable selection to select the Markov blanket, before a DAG search stage. Finally, we show how L1 variable selection can be used inside of an order search algorithm. The effectiveness of these L1based approaches are compared to current state of the art methods on 10 datasets.
Structure Learning of Bayesian Networks using Constraints
"... This paper addresses exact learning of Bayesian network structure from data and expert’s knowledge based on score functions that are decomposable. First, it describes useful properties that strongly reduce the time and memory costs of many known methods such as hillclimbing, dynamic programming and ..."
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Cited by 19 (1 self)
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This paper addresses exact learning of Bayesian network structure from data and expert’s knowledge based on score functions that are decomposable. First, it describes useful properties that strongly reduce the time and memory costs of many known methods such as hillclimbing, dynamic programming and sampling variable orderings. Secondly, a branch and bound algorithm is presented that integrates parameter and structural constraints with data in a way to guarantee global optimality with respect to the score function. It is an anytime procedure because, if stopped, it provides the best current solution and an estimation about how far it is from the global solution. We show empirically the advantages of the properties and the constraints, and the applicability of the algorithm to large data sets (up to one hundred variables) that cannot be handled by other current methods (limited to around 30 variables). 1.
Efficient markov network structure discovery using independence tests
 In Proc SIAM Data Mining
, 2006
"... We present two algorithms for learning the structure of a Markov network from discrete data: GSMN and GSIMN. Both algorithms use statistical conditional independence tests on data to infer the structure by successively constraining the set of structures consistent with the results of these tests. GS ..."
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Cited by 16 (1 self)
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We present two algorithms for learning the structure of a Markov network from discrete data: GSMN and GSIMN. Both algorithms use statistical conditional independence tests on data to infer the structure by successively constraining the set of structures consistent with the results of these tests. GSMN is a natural adaptation of the GrowShrink algorithm of Margaritis and Thrun for learning the structure of Bayesian networks. GSIMN extends GSMN by additionally exploiting Pearl’s wellknown properties of conditional independence relations to infer novel independencies from known independencies, thus avoiding the need to perform these tests. Experiments on artificial and real data sets show GSIMN can yield savings of up to 70 % with respect to GSMN, while generating a Markov network with comparable or in several cases considerably improved quality. In addition
Modelling Activity Global Temporal Dependencies using Time Delayed Probabilistic Graphical Model
"... We present a novel approach for detecting global behaviour anomalies in multiple disjoint cameras by learning time delayed dependencies between activities cross camera views. Specifically, we propose to model multicamera activities using a Time Delayed Probabilistic Graphical Model (TDPGM) with di ..."
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Cited by 15 (2 self)
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We present a novel approach for detecting global behaviour anomalies in multiple disjoint cameras by learning time delayed dependencies between activities cross camera views. Specifically, we propose to model multicamera activities using a Time Delayed Probabilistic Graphical Model (TDPGM) with different nodes representing activities in different semantically decomposed regions from different camera views, and the directed links between nodes encoding causal relationships between the activities. A novel twostage structure learning algorithm is formulated to learn globally optimised timedelayed dependencies. A new cumulative abnormality score is also introduced to replace the conventional loglikelihood score for gaining significantly more robust and reliable realtime anomaly detection. The effectiveness of the proposed approach is validated using a camera network installed at a busy underground station. 1.
Bayesian structure learning using dynamic programming and MCMC
 In UAI, 2007b
"... We show how to significantly speed up MCMC sampling of DAG structures by using a powerful nonlocal proposal based on Koivisto’s dynamic programming (DP) algorithm (11; 10), which computes the exact marginal posterior edge probabilities by analytically summing over orders. Furthermore, we show how s ..."
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Cited by 14 (1 self)
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We show how to significantly speed up MCMC sampling of DAG structures by using a powerful nonlocal proposal based on Koivisto’s dynamic programming (DP) algorithm (11; 10), which computes the exact marginal posterior edge probabilities by analytically summing over orders. Furthermore, we show how sampling in DAG space can avoid subtle biases that are introduced by approaches that work only with orders, such as Koivisto’s DP algorithm and MCMC order samplers (6; 5). 1
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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Cited by 6 (6 self)
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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.
Optimal search on clustered structural constraint for learning Bayesian network structure
 Journal of Machine Learning Research
"... We study the problem of learning an optimal Bayesian network in a constrained search space; skeletons are compelled to be subgraphs of a given undirected graph called the superstructure. The previously derived constrained optimal search (COS) remains limited even for sparse superstructures. To exte ..."
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Cited by 5 (0 self)
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We study the problem of learning an optimal Bayesian network in a constrained search space; skeletons are compelled to be subgraphs of a given undirected graph called the superstructure. The previously derived constrained optimal search (COS) remains limited even for sparse superstructures. To extend its feasibility, we propose to divide the superstructure into several clusters and perform an optimal search on each of them. Further, to ensure acyclicity, we introduce the concept of ancestral constraints (ACs) and derive an optimal algorithm satisfying a given set of ACs. Finally, we theoretically derive the necessary and sufficient sets of ACs to be considered for finding an optimal constrained graph. Empirical evaluations demonstrate that our algorithm can learn optimal Bayesian networks for some graphs containing several hundreds of vertices, and even for superstructures having a high average degree (up to four), which is a drastic improvement in feasibility over the previous optimal algorithm. Learnt networks are shown to largely outperform stateoftheart heuristic algorithms both in terms of score and structural hamming distance.
A Recursive Method for Structural Learning of Directed Acyclic Graphs
"... In this paper, we propose a recursive method for structural learning of directed acyclic graphs (DAGs), in which a problem of structural learning for a large DAG is first decomposed into two problems of structural learning for two small vertex subsets, each of which is then decomposed recursively in ..."
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Cited by 4 (1 self)
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In this paper, we propose a recursive method for structural learning of directed acyclic graphs (DAGs), in which a problem of structural learning for a large DAG is first decomposed into two problems of structural learning for two small vertex subsets, each of which is then decomposed recursively into two problems of smaller subsets until none subset can be decomposed further. In our approach, search for separators of a pair of variables in a large DAG is localized to small subsets, and thus the approach can improve the efficiency of searches and the power of statistical tests for structural learning. We show how the recent advances in the learning of undirected graphical models can be employed to facilitate the decomposition. Simulations are given to demonstrate the performance of the proposed method.