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Learning Bayesian Network Structure using LP Relaxations
"... We propose to solve the combinatorial problem of finding the highest scoring Bayesian network structure from data. This structure learning problem can be viewed as an inference problem where the variables specify the choice of parents for each node in the graph. The key combinatorial difficulty aris ..."
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Cited by 58 (2 self)
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We propose to solve the combinatorial problem of finding the highest scoring Bayesian network structure from data. This structure learning problem can be viewed as an inference problem where the variables specify the choice of parents for each node in the graph. The key combinatorial difficulty arises from the global constraint that the graph structure has to be acyclic. We cast the structure learning problem as a linear program over the polytope defined by valid acyclic structures. In relaxing this problem, we maintain an outer bound approximation to the polytope and iteratively tighten it by searching over a new class of valid constraints. If an integral solution is found, it is guaranteed to be the optimal Bayesian network. When the relaxation is not tight, the fast dual algorithms we develop remain useful in combination with a branch and bound method. Empirical results suggest that the method is competitive or faster than alternative exact methods based on dynamic programming. 1
Bayesian network learning with cutting planes.
 In Proceedings of the TwentySeventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI11),
, 2011
"... Abstract The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises log marginal likelihood (BDe score). Integer ..."
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Cited by 46 (7 self)
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Abstract The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises log marginal likelihood (BDe score). Integer programming, specifically the SCIP framework, is used to solve this optimisation problem. Acyclicity constraints are added to the integer program (IP) during solving in the form of cutting planes. Finding good cutting planes is the key to the success of the approachthe search for such cutting planes is effected using a subIP. Results show that this is a particularly fast method for exact BN learning.
Efficient structure learning of Bayesian networks using constraints
 Journal of Machine Learning Research
"... This paper addresses the problem of learning Bayesian network structures from data based on score functions that are decomposable. It describes properties that strongly reduce the time and memory costs of many known methods without losing global optimality guarantees. These properties are derived fo ..."
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Cited by 30 (7 self)
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This paper addresses the problem of learning Bayesian network structures from data based on score functions that are decomposable. It describes properties that strongly reduce the time and memory costs of many known methods without losing global optimality guarantees. These properties are derived for different score criteria such as Minimum Description Length (or Bayesian Information Criterion), Akaike Information Criterion and Bayesian Dirichlet Criterion. Then a branchandbound algorithm is presented that integrates structural constraints with data in a way to guarantee global optimality. As an example, structural constraints are used to map the problem of structure learning in Dynamic Bayesian networks into a corresponding augmented Bayesian network. Finally, we show empirically the benefits of using the properties with stateoftheart methods and with the new algorithm, which is able to handle larger data sets than before.
Improving the scalability of optimal Bayesian network learning with externalmemory frontier breadthfirst branch and bound search
 IN PROCEEDINGS OF THE 27TH CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
"... Previous work has shown that the problem of learning the optimal structure of a Bayesian network can be formulated as a shortest path finding problem in a graph and solved using A* search. In this paper, we improve the scalability of this approach by developing a memoryefficient heuristic search ..."
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Cited by 17 (9 self)
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Previous work has shown that the problem of learning the optimal structure of a Bayesian network can be formulated as a shortest path finding problem in a graph and solved using A* search. In this paper, we improve the scalability of this approach by developing a memoryefficient heuristic search algorithm for learning the structure of a Bayesian network. Instead of using A*, we propose a frontier breadthfirst branch and bound search that leverages the layered structure of the search graph of this problem so that no more than two layers of the graph, plus solution reconstruction information, need to be stored in memory at a time. To further improve scalability, the algorithm stores most of the graph in external memory, such as hard disk, when it does not fit in RAM. Experimental results show that the resulting algorithm solves significantly larger problems than the current state of the art.
Learning optimal Bayesian networks using A* search
 In Proceedings of the 22nd International Joint Conference on Artificial Intelligence
, 2011
"... This paper formulates learning optimal Bayesian network as a shortest path finding problem. An A* search algorithm is introduced to solve the problem. With the guidance of a consistent heuristic, the algorithm learns an optimal Bayesian network by only searching the most promising parts of the solu ..."
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Cited by 16 (7 self)
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This paper formulates learning optimal Bayesian network as a shortest path finding problem. An A* search algorithm is introduced to solve the problem. With the guidance of a consistent heuristic, the algorithm learns an optimal Bayesian network by only searching the most promising parts of the solution space. Empirical results show that the A* search algorithm significantly improves the time and space efficiency of existing methods on a set of benchmark datasets. 1
Incremental activity modelling in multiple disjoint cameras
 IEEE Transactions on Pattern Analysis and Machine Intelligence
"... Abstract—Activity modeling and unusual event detection in a network of cameras is challenging, particularly when the camera views are not overlapped. We show that it is possible to detect unusual events in multiple disjoint cameras as contextincoherent patterns through incremental learning of time ..."
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Cited by 13 (7 self)
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Abstract—Activity modeling and unusual event detection in a network of cameras is challenging, particularly when the camera views are not overlapped. We show that it is possible to detect unusual events in multiple disjoint cameras as contextincoherent patterns through incremental learning of time delayed dependencies between distributed local activities observed within and across camera views. Specifically, we model multicamera activities using a Time Delayed Probabilistic Graphical Model (TDPGM) with different nodes representing activities in different decomposed regions from different views and the directed links between nodes encoding their time delayed dependencies. To deal with visual context changes, we formulate a novel incremental learning method for modeling time delayed dependencies that change over time. We validate the effectiveness of the proposed approach using a synthetic data set and videos captured from a camera network installed at a busy underground station. Index Terms—Unusual event detection, multicamera activity modeling, time delay estimation, incremental structure learning. Ç 1
Capturing complex spatiotemporal relations among facial muscles for facial expression recognition
 In CVPR
, 2013
"... Spatialtemporal relations among facial muscles carry crucial information about facial expressions yet have not been thoroughly exploited. One contributing factor for this is the limited ability of the current dynamic models in capturing complex spatial and temporal relations. Existing dynamic mod ..."
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Cited by 13 (1 self)
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Spatialtemporal relations among facial muscles carry crucial information about facial expressions yet have not been thoroughly exploited. One contributing factor for this is the limited ability of the current dynamic models in capturing complex spatial and temporal relations. Existing dynamic models can only capture simple local temporal relations among sequential events, or lack the ability for incorporating uncertainties. To overcome these limitations and take full advantage of the spatiotemporal information, we propose to model the facial expression as a complex activity that consists of temporally overlapping or sequential primitive facial events. We further propose the Interval Temporal Bayesian Network to capture these complex temporal relations among primitive facial events for facial expression modeling and recognition. Experimental results on benchmark databases demonstrate the feasibility of the proposed approach in recognizing facial expressions based purely on spatiotemporal relations among facial muscles, as well as its advantage over the existing methods. 1.
Properties of bayesian dirichlet scores to learn bayesian network structures
 In TwentyFourth AAAI Conference on Aritificial Intelligence (AAAI10
, 2010
"... This paper addresses exact learning of Bayesian network structure from data based on the Bayesian Dirichlet score function and its derivations. We describe useful properties that strongly reduce the computational costs of many known methods without losing global optimality guarantees. We show empiri ..."
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Cited by 9 (2 self)
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This paper addresses exact learning of Bayesian network structure from data based on the Bayesian Dirichlet score function and its derivations. We describe useful properties that strongly reduce the computational costs of many known methods without losing global optimality guarantees. We show empirically the advantages of the properties in terms of time and memory consumptions, demonstrating that stateoftheart methods, with the use of such properties, might handle larger data sets than those currently possible.
Learning Bounded Treewidth Bayesian Networks using Integer Linear Programming
, 2014
"... In many applications one wants to compute conditional probabilities given a Bayesian network. This inference problem is NPhard in general but becomes tractable when the network has low treewidth. Since the inference problem is common in many application areas, we provide a practical algorithm for ..."
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Cited by 9 (1 self)
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In many applications one wants to compute conditional probabilities given a Bayesian network. This inference problem is NPhard in general but becomes tractable when the network has low treewidth. Since the inference problem is common in many application areas, we provide a practical algorithm for learning bounded treewidth Bayesian networks. We cast this problem as an integer linear program (ILP). The program can be solved by an anytime algorithm which provides upper bounds to assess the quality of the found solutions. A key component of our program is a novel integer linear formulation for bounding treewidth of a graph. Our tests clearly indicate that our approach works in practice, as our implementation was able to find an optimal or nearly optimal network for most of the data sets.
Evaluating Anytime Algorithms for Learning Optimal Bayesian Networks
 In Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence (UAI13
, 2013
"... Exact algorithms for learning Bayesian networks guarantee to find provably optimal networks. However, they may fail in difficult learning tasks due to limited time or memory. In this research we adapt several anytime heuristic searchbased algorithms to learn Bayesian networks. These algorithms find ..."
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Cited by 9 (4 self)
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Exact algorithms for learning Bayesian networks guarantee to find provably optimal networks. However, they may fail in difficult learning tasks due to limited time or memory. In this research we adapt several anytime heuristic searchbased algorithms to learn Bayesian networks. These algorithms find highquality solutions quickly, and continually improve the incumbent solution or prove its optimality before resources are exhausted. Empirical results show that the anytime window A * algorithm usually finds higherquality, often optimal, networks more quickly than other approaches. The results also show that, surprisingly, while generating networks with few parents per variable are structurally simpler, they are harder to learn than complex generating networks with more parents per variable. 1