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87
Dynamic Bayesian Networks: Representation, Inference and Learning
, 2002
"... Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have bee ..."
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Cited by 757 (3 self)
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Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs
and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linearGaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data.
In particular, the main novel technical contributions of this thesis are as follows: a way of representing
Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of
applying RaoBlackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization
and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.
Probability product kernels
 Journal of Machine Learning Research
, 2004
"... The advantages of discriminative learning algorithms and kernel machines are combined with generative modeling using a novel kernel between distributions. In the probability product kernel, data points in the input space are mapped to distributions over the sample space and a general inner product i ..."
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Cited by 179 (9 self)
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The advantages of discriminative learning algorithms and kernel machines are combined with generative modeling using a novel kernel between distributions. In the probability product kernel, data points in the input space are mapped to distributions over the sample space and a general inner product is then evaluated as the integral of the product of pairs of distributions. The kernel is straightforward to evaluate for all exponential family models such as multinomials and Gaussians and yields interesting nonlinear kernels. Furthermore, the kernel is computable in closed form for latent distributions such as mixture models, hidden Markov models and linear dynamical systems. For intractable models, such as switching linear dynamical systems, structured meanfield approximations can be brought to bear on the kernel evaluation. For general distributions, even if an analytic expression for the kernel is not feasible, we show a straightforward sampling method to evaluate it. Thus, the kernel permits discriminative learning methods, including support vector machines, to exploit the properties, metrics and invariances of the generative models we infer from each datum. Experiments are shown using multinomial models for text, hidden Markov models for biological data sets and linear dynamical systems for time series data.
Tracking Articulated Body by Dynamic Markov Network
 PROC. IEEE INT'L CONF. ON COMPUTER VISION, NICE, FRANCE
, 2003
"... A new method for visual tracking of articulated objects is presented. Analyzing articulated motion is challenging because the dimensionality increase potentially demands tremendous increase of computation. To ease this problem, we propose an approach that analyzes subparts locally while reinforcing ..."
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Cited by 59 (9 self)
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A new method for visual tracking of articulated objects is presented. Analyzing articulated motion is challenging because the dimensionality increase potentially demands tremendous increase of computation. To ease this problem, we propose an approach that analyzes subparts locally while reinforcing the structural constraints at the mean time. The computational model of the proposed approach is based on a dynamic Markov network, a generative model which characterizes the dynamics and the image observations of each individual subpart as well as the motion constraints among different subparts. Probabilistic variational analysis of the model reveals a mean field approximation to the posterior densities of each subparts given visual evidence, and provides a computationally efficient way for such a difficult Bayesian inference problem. In addition, we design mean field Monte Carlo (MFMC) algorithms, in which a set of low dimensional particle filters interact with each other and solve the high dimensional problem collaboratively. Extensive experiments on tracking human body parts demonstrate the effectiveness, significance and computational efficiency of the proposed method.
Gaussian process approximation of stochastic differential equations
 Journal of Machine Learning Research, Workshop and Conference Proceedings
, 2007
"... Some of the most complex models routinely run are numerical weather prediction models. These models are based on a discretisation of a coupled set of partial differential equations (the dynamics) which govern the time evolution of the atmosphere, described in terms of temperature, pressure, velocity ..."
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Cited by 45 (10 self)
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Some of the most complex models routinely run are numerical weather prediction models. These models are based on a discretisation of a coupled set of partial differential equations (the dynamics) which govern the time evolution of the atmosphere, described in terms of temperature, pressure, velocity,
Supplement to “Uncovering latent structure in valued graphs: A variational approach.” DOI
, 2010
"... ar ..."
Supervised Link Prediction Using Multiple Sources
"... Abstract—Link prediction is a fundamental problem in social network analysis and modernday commercial applications such as Facebook and Myspace. Most existing research approaches this problem by exploring the topological structure of a social network using only one source of information. However, i ..."
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Cited by 20 (3 self)
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Abstract—Link prediction is a fundamental problem in social network analysis and modernday commercial applications such as Facebook and Myspace. Most existing research approaches this problem by exploring the topological structure of a social network using only one source of information. However, in many application domains, in addition to the social network of interest, there are a number of auxiliary social networks and/or derived proximity networks available. The contribution of the paper is twofold: (1) a supervised learning framework that can effectively and efficiently learn the dynamics of social networks in the presence of auxiliary networks; (2) a feature design scheme for constructing a rich variety of pathbased features using multiple sources, and an effective feature selection strategy based on structured sparsity. Extensive experiments on three realworld collaboration networks show that our model can effectively learn to predict new links using multiple sources, yielding higher prediction accuracy than unsupervised and singlesource supervised models. Index Terms—social network; link prediction; multiple sources; supervised learning; I.
A SpatioTemporal Approach to Collaborative Filtering
"... In this paper, we propose a novel spatiotemporal model for collaborative filtering applications. Our model is based on lowrank matrix factorization that uses a spatiotemporal filtering approach to estimate user and item factors. The spatial component regularizes the factors by exploiting correlat ..."
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Cited by 19 (2 self)
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In this paper, we propose a novel spatiotemporal model for collaborative filtering applications. Our model is based on lowrank matrix factorization that uses a spatiotemporal filtering approach to estimate user and item factors. The spatial component regularizes the factors by exploiting correlation across users and/or items, modeled as a function of some implicit feedback (e.g., who rated what) and/or some side information (e.g., user demographics, browsing history). In particular, we incorporate correlation in factors through a Markov random field prior in a probabilistic framework, whereby the neighborhood weights are functions of user and item covariates. The temporal component ensures that the user/item factors adapt to process changes that occur through time and is implemented in a state space framework with fast estimation through Kalman filtering. Our spatiotemporal filtering (STKF hereafter) approach provides a single joint model to simultaneously incorporate both spatial and temporal structure in ratings and therefore provides an accurate method to predict future ratings. To ensure scalability of STKF, we employ a meanfield approximation for inference. Incorporating user/item covariates in estimating neighborhood weights also helps in dealing with both coldstart and warmstart problems seamlessly in a single unified modeling framework; covariates predict factors for new users and items through the neighborhood. We illustrate our method on simulated data, benchmark data and data obtained from a relatively new recommender system application arising in the context of Yahoo! Front Page.
A Statistical Field Model for Pedestrian Detection
 CVPR 2005. Vol I
"... This paper presents a new statistical model for detecting and tracking deformable objects such as pedestrians, where large shape variations induced by local shape deformation can not be well captured by global methods such as PCA. The proposed model employs a Boltzmann distribution to capture the pr ..."
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Cited by 18 (3 self)
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This paper presents a new statistical model for detecting and tracking deformable objects such as pedestrians, where large shape variations induced by local shape deformation can not be well captured by global methods such as PCA. The proposed model employs a Boltzmann distribution to capture the prior of local deformation, and embeds it into a Markov network which can be learned from data. A mean field variational analysis of this model provides computationally efficient algorithms for computing the likelihood of image observations and facilitate fast model training. Based on that, effective detection and tracking algorithms for deformable objects are proposed and applied to pedestrian detection and tracking. The proposed method has several advantages. Firstly, it captures local deformation well and thus is robust to occlusions and clutter. In addition, it is computationally tractable. Moreover, it divides deformation into local deformation and global deformation, then conquers them by combining bottomup and topdown methodologies. Extensive experiments demonstrate the effectiveness of the proposed model for deformable objects. 1
Bayesian Ying Yang system, best harmony learning, and Gaussian manifold based family
 Computational Intelligence: Research Frontiers, WCCI2008 Plenary/Invited Lectures. Lecture Notes in Computer Science
"... five action circling ..."
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A probabilistic methodology for integrating knowledge and experiments on biological networks
 J. Comput
, 2006
"... Biological systems are traditionally studied by focusing on a specific subsystem, building an intuitive model for it, and refining the model using results from carefully designed experiments. Modern experimental techniques provide massive data on the global behavior of biological systems, and system ..."
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Cited by 11 (2 self)
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Biological systems are traditionally studied by focusing on a specific subsystem, building an intuitive model for it, and refining the model using results from carefully designed experiments. Modern experimental techniques provide massive data on the global behavior of biological systems, and systematically using these large datasets for refining existing knowledge is a major challenge. Here we introduce an extended computational framework that combines formalization of existing qualitative models, probabilistic modeling, and integration of highthroughput experimental data. Using our methods, it is possible to interpret genomewide measurements in the context of prior knowledge on the system, to assign statistical meaning to the accuracy of such knowledge, and to learn refined models with improved fit to the experiments. Our model is represented as a probabilistic factor graph, and the framework accommodates partial measurements of diverse biological elements. We study the performance of several probabilistic inference algorithms and show that hidden model variables can be reliably inferred even in the presence of feedback loops and complex logic. We show how to refine prior knowledge on combinatorial regulatory relations using hypothesis testing and derive pvalues for learned model features. We test our methodology and algorithms on a simulated model and on two real yeast models. In particular, we use our method to explore uncharacterized relations among regulators in the yeast response to hyperosmotic shock and in the yeast lysine biosynthesis system. Our integrative approach to the analysis of biological regulation is demonstrated to synergistically combine qualitative and quantitative evidence into concrete biological predictions. Key words: biological systems, probabilistic modeling, high throughput data. 1.