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61
The Bayes Net Toolbox for MATLAB
 Computing Science and Statistics
, 2001
"... The Bayes Net Toolbox (BNT) is an opensource Matlab package for directed graphical models. BNT supports many kinds of nodes (probability distributions), exact and approximate inference, parameter and structure learning, and static and dynamic models. BNT is widely used in teaching and research: the ..."
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Cited by 243 (1 self)
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The Bayes Net Toolbox (BNT) is an opensource Matlab package for directed graphical models. BNT supports many kinds of nodes (probability distributions), exact and approximate inference, parameter and structure learning, and static and dynamic models. BNT is widely used in teaching and research: the web page has received over 28,000 hits since May 2000. In this paper, we discuss a broad spectrum of issues related to graphical models (directed and undirected), and describe, at a highlevel, how BNT was designed to cope with them all. We also compare BNT to other software packages for graphical models, and to the nascent OpenBayes effort.
FABMAP: Probabilistic localization and mapping in the space of
 Journal of Field Robotics DOI 10.1002/rob 914 • Journal of Field Robotics—2009 appearance. International Journal of Robotics Research
"... This paper describes a probabilistic approach to the problem of recognizing places based on their appearance. The system we present is not limited to localization, but can determine that a new observation comes from a previously unseen place, and so augment its map. Effectively this is a SLAM syst ..."
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Cited by 180 (13 self)
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This paper describes a probabilistic approach to the problem of recognizing places based on their appearance. The system we present is not limited to localization, but can determine that a new observation comes from a previously unseen place, and so augment its map. Effectively this is a SLAM system in the space of appearance. Our probabilistic approach allows us to explicitly account for perceptual aliasing in the environment—identical but indistinctive observations receive a low probability of having come from the same place. We achieve this by learning a generative model of place appearance. By partitioning the learning problem into two parts, new place models can be learned online from only a single observation of a place. The algorithm complexity is linear in the number of places in the map, and is particularly suitable for online loop closure detection in mobile robotics. KEY WORDS—place recognition, topological SLAM, appearance based navigation 1.
Efficient structure learning of Markov networks using L1regularization
 In NIPS
, 2006
"... Markov networks are widely used in a wide variety of applications, in problems ranging from computer vision, to natural language, to computational biology. In most current applications, even those that rely heavily on learned models, the structure of the Markov network is constructed by hand, due to ..."
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Cited by 146 (3 self)
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Markov networks are widely used in a wide variety of applications, in problems ranging from computer vision, to natural language, to computational biology. In most current applications, even those that rely heavily on learned models, the structure of the Markov network is constructed by hand, due to the lack of effective algorithms for learning Markov network structure from data. In this paper, we provide a computationally effective method for learning Markov network structure from data. Our method is based on the use of L1 regularization on the weights of the loglinear model, which has the effect of biasing the model towards solutions where many of the parameters are zero. This formulation converts the Markov network learning problem into a convex optimization problem in a continuous space, which can be solved using efficient gradient methods. A key issue in this setting is the (unavoidable) use of approximate inference, which can lead to errors in the gradient computation when the network structure is dense. Thus, we explore the use of different feature introduction schemes and compare their performance. We provide results for our method on synthetic data, and on two real world data sets: modeling the joint distribution of pixel values in the MNIST data, and modeling the joint distribution of genetic sequence variations in the human HapMap data. We show that our L1based method achieves considerably higher generalization performance than the more standard L2based method (a Gaussian parameter prior) or pure maximumlikelihood learning. We also show that we can learn MRF network structure at a computational cost that is not much greater than learning parameters alone, demonstrating the existence of a feasible method for this important problem. 1
Thin Junction Tree Filters for Simultaneous Localization and Mapping
 In Intl. Joint Conf. on Artificial Intelligence (IJCAI
, 2003
"... Simultaneous Localization and Mapping (SLAM) is a fundamental problem in mobile robotics: while a robot navigates in an unknown environment, it must incrementally build a map of its surroundings and localize itself within that map. Traditional approaches to the problem are based upon Kalman filters, ..."
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Cited by 137 (1 self)
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Simultaneous Localization and Mapping (SLAM) is a fundamental problem in mobile robotics: while a robot navigates in an unknown environment, it must incrementally build a map of its surroundings and localize itself within that map. Traditional approaches to the problem are based upon Kalman filters, but suffer from complexity issues: the size of the belief state and the time complexity of the filtering operation grow quadratically in the size of the map. This paper presents a filtering technique that maintains a tractable approximation of the filtered belief state as a thin junction tree. The junction tree grows under measurement and motion updates and is periodically "thinned" to remain tractable via efficient maximum likelihood projections. When applied to the SLAM problem, these thin junction tree filters have a linearspace belief state representation, and use a lineartime filtering operation. Further approximation can yield a constanttime filtering operation, at the expense of delaying the incorporation of observations into the majority of the map. Experiments on a suite of SLAM problems validate the approach.
Learning Associative Markov Networks
 Proc. ICML
, 2004
"... Markov networks are extensively used to model complex sequential, spatial, and relational interactions in fields as diverse as image processing, natural language analysis, and bioinformatics. ..."
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Cited by 99 (10 self)
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Markov networks are extensively used to model complex sequential, spatial, and relational interactions in fields as diverse as image processing, natural language analysis, and bioinformatics.
Learning factor graphs in polynomial time and sample complexity
 JMLR
, 2006
"... We study the computational and sample complexity of parameter and structure learning in graphical models. Our main result shows that the class of factor graphs with bounded degree can be learned in polynomial time and from a polynomial number of training examples, assuming that the data is generated ..."
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Cited by 65 (0 self)
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We study the computational and sample complexity of parameter and structure learning in graphical models. Our main result shows that the class of factor graphs with bounded degree can be learned in polynomial time and from a polynomial number of training examples, assuming that the data is generated by a network in this class. This result covers both parameter estimation for a known network structure and structure learning. It implies as a corollary that we can learn factor graphs for both Bayesian networks and Markov networks of bounded degree, in polynomial time and sample complexity. Importantly, unlike standard maximum likelihood estimation algorithms, our method does not require inference in the underlying network, and so applies to networks where inference is intractable. We also show that the error of our learned model degrades gracefully when the generating distribution is not a member of the target class of networks. In addition to our main result, we show that the sample complexity of parameter learning in graphical models has an O(1) dependence on the number of variables in the model when using the KLdivergence normalized by the number of variables as the performance criterion.
Structure learning in random fields for heart motion abnormality detection
 In CVPR
, 2008
"... Coronary Heart Disease can be diagnosed by assessing the regional motion of the heart walls in ultrasound images of the left ventricle. Even for experts, ultrasound images are difficult to interpret leading to high intraobserver variability. Previous work indicates that in order to approach this pr ..."
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Cited by 59 (8 self)
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Coronary Heart Disease can be diagnosed by assessing the regional motion of the heart walls in ultrasound images of the left ventricle. Even for experts, ultrasound images are difficult to interpret leading to high intraobserver variability. Previous work indicates that in order to approach this problem, the interactions between the different heart regions and their overall influence on the clinical condition of the heart need to be considered. To do this, we propose a method for jointly learning the structure and parameters of conditional random fields, formulating these tasks as a convex optimization problem. We consider blockL1 regularization for each set of features associated with an edge, and formalize an efficient projection method to find the globally optimal penalized maximum likelihood solution. We perform extensive numerical experiments comparing the presented method with related methods that approach the structure learning problem differently. We verify the robustness of our method on echocardiograms collected in routine clinical practice at one hospital. 1.
Efficient Principled Learning of Thin Junction Trees
"... We present the first truly polynomial algorithm for PAClearning the structure of boundedtreewidth junction trees – an attractive subclass of probabilistic graphical models that permits both the compact representation of probability distributions and efficient exact inference. For a constant treewi ..."
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Cited by 48 (3 self)
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We present the first truly polynomial algorithm for PAClearning the structure of boundedtreewidth junction trees – an attractive subclass of probabilistic graphical models that permits both the compact representation of probability distributions and efficient exact inference. For a constant treewidth, our algorithm has polynomial time and sample complexity. If a junction tree with sufficiently strong intraclique dependencies exists, we provide strong theoretical guarantees in terms of KL divergence of the result from the true distribution. We also present a lazy extension of our approach that leads to very significant speed ups in practice, and demonstrate the viability of our method empirically, on several real world datasets. One of our key new theoretical insights is a method for bounding the conditional mutual information of arbitrarily large sets of variables with only polynomially many mutual information computations on fixedsize subsets of variables, if the underlying distribution can be approximated by a boundedtreewidth junction tree. 1
Hingeloss Markov Random Fields: Convex Inference for Structured Prediction
 In Uncertainty in Artificial Intelligence
, 2013
"... Graphical models for structured domains are powerful tools, but the computational complexities of combinatorial prediction spaces can force restrictions on models, or require approximate inference in order to be tractable. Instead of working in a combinatorial space, we use hingeloss Markov random ..."
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Cited by 26 (18 self)
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Graphical models for structured domains are powerful tools, but the computational complexities of combinatorial prediction spaces can force restrictions on models, or require approximate inference in order to be tractable. Instead of working in a combinatorial space, we use hingeloss Markov random fields (HLMRFs), an expressive class of graphical models with logconcave density functions over continuous variables, which can represent confidences in discrete predictions. This paper demonstrates that HLMRFs are general tools for fast and accurate structured prediction. We introduce the first inference algorithm that is both scalable and applicable to the full class of HLMRFs, and show how to train HLMRFs with several learning algorithms. Our experiments show that HLMRFs match or surpass the predictive performance of stateoftheart methods, including discrete models, in four application domains. 1
Rapid protein sidechain packing via tree decomposition
 Research in Computational Molecular Biology, Lecture Notes in Computer Science
, 2005
"... Abstract. This paper proposes a novel tree decomposition based sidechain assignment algorithm, which can obtain the globally optimal solution of the sidechain packing problem very efficiently. Theoretically, the computational complexity of this algorithm is O((N +M)n tw+1 rot) where N is the numbe ..."
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Cited by 25 (1 self)
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Abstract. This paper proposes a novel tree decomposition based sidechain assignment algorithm, which can obtain the globally optimal solution of the sidechain packing problem very efficiently. Theoretically, the computational complexity of this algorithm is O((N +M)n tw+1 rot) where N is the number of residues in the protein, M the number of interacting residue pairs, nrot the average number of rotamers for each residue and tw( = O(N 2 3 log N)) the tree width of the residue interaction graph. Based on this algorithm, we have developed a sidechain prediction program SCATD (Side Chain Assignment via Tree Decomposition). Experimental results show that after the Goldstein DEE is conducted, nrot is around 3.5, tw is only 3 or 4 for most of the test proteins in the SCWRL benchmark and less than 10 for all the test proteins. SCATD runs up to 90 times faster than SCWRL 3.0 on some large proteins in the SCWRL benchmark and achieves an average of five times faster speed on all the test proteins. If only the postDEE stage is taken into consideration, then our treedecomposition based energy minimization algorithm is more than 200 times faster than that in SCWRL 3.0 on some large proteins. SCATD is freely available for academic research upon request. 1