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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 564 (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.
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 176 (2 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.
The maxmin hillclimbing bayesian network structure learning algorithm
 Machine Learning
, 2006
"... Abstract. We present a new algorithm for Bayesian network structure learning, called MaxMin HillClimbing (MMHC). The algorithm combines ideas from local learning, constraintbased, and searchandscore techniques in a principled and effective way. It first reconstructs the skeleton of a Bayesian n ..."
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Cited by 76 (7 self)
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Abstract. We present a new algorithm for Bayesian network structure learning, called MaxMin HillClimbing (MMHC). The algorithm combines ideas from local learning, constraintbased, and searchandscore techniques in a principled and effective way. It first reconstructs the skeleton of a Bayesian network and then performs a Bayesianscoring greedy hillclimbing search to orient the edges. In our extensive empirical evaluation MMHC outperforms on average and in terms of various metrics several prototypical and stateoftheart algorithms, namely the PC, Sparse Candidate, Three Phase Dependency Analysis, Optimal Reinsertion, Greedy Equivalence Search, and Greedy Search. These are the first empirical results simultaneously comparing most of the major Bayesian network algorithms against each other. MMHC offers certain theoretical advantages, specifically over the Sparse Candidate algorithm, corroborated by our experiments. MMHC and detailed results of our study are publicly available at
Autosupervised learning in the Bayesian programming framework
 in The AAAI Spring Symposium on Developmental Robotics
, 2005
"... Abstract — Domestic and real world robotics requires continuous learning of new skills and behaviors to interact with humans. Autosupervised learning, a compromise between supervised and completely unsupervised learning, consist in relying on previous knowledge to acquire new skills. We propose her ..."
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Cited by 5 (0 self)
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Abstract — Domestic and real world robotics requires continuous learning of new skills and behaviors to interact with humans. Autosupervised learning, a compromise between supervised and completely unsupervised learning, consist in relying on previous knowledge to acquire new skills. We propose here to realize autosupervised learning by exploiting statistical regularities in the sensorimotor space of a robot. In our context, it corresponds to achieve feature selection in a Bayesian programming framework. We compare several feature selection algorithms and validate them on a real robotic experiment.
DistributionFree Learning of Graphical Model Structure in Continuous Domains
, 2004
"... In this paper we present a probabilistic nonparametric conditional independence test of X and Y given a third variable Z in domains where X, Y, and Z are continuous. This test can be used for the induction of the structure of a graphical model (such as a Bayesian or Markov network) from experimenta ..."
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In this paper we present a probabilistic nonparametric conditional independence test of X and Y given a third variable Z in domains where X, Y, and Z are continuous. This test can be used for the induction of the structure of a graphical model (such as a Bayesian or Markov network) from experimental data. We also provide an effective method for calculating it from data. We show that our method works well in practice on artificial benchmark data sets constructed from a diverse set of functions. We also demonstrate learning of the structure of a graphical model in a continuous domain from realworld data, to our knowledge for the first time using independencebased methods and without any distributional assumptions. 1.1 Motivation and Related Work Conditional independence of X and Y given a third variable Z is defined as independence of X and Y for every value z of Z almost surely i.e., except a subset of zero probability (Lauritzen, 1996). In this paper we address the problem of testing for conditional independence when the variables X, Y, and Z are continuous. Such a test can be used as a key building block
Greedy PartWise Learning of SumProduct Networks
"... Abstract. Sumproduct networks allow to model complex variable interactions while still granting efficient inference. However, the learning algorithms proposed so far are explicitly or implicitly restricted to the image domain, either by assuming variable neighborhood or by assuming that dependent v ..."
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Abstract. Sumproduct networks allow to model complex variable interactions while still granting efficient inference. However, the learning algorithms proposed so far are explicitly or implicitly restricted to the image domain, either by assuming variable neighborhood or by assuming that dependent variables are related by their values over the training set. In this paper, we introduce a novel algorithm, learning the structure and parameters of sumproduct networks in a greedy bottomup manner. Our algorithm subsequently merges probabilistic models of small variable scope to larger and more complex models. These merges are guided by statistical dependence test, and parameters are learned using a maximum mutual information principle. In experiments we show that our method competes well with the existing learning algorithms for sumproduct networks on the task of reconstructing covered image regions, and outperforms these when neither neighborhood nor variable relation by value can be assumed. 1
Maximum Likelihood Quantization of Genomic Features using Dynamic Programming
"... Dynamic programming is introduced to quantize a continuous random variable into a discrete random variable. Quantization is often useful before statistical analysis or reconstruction of large network models among multiple random variables. The quantization, through dynamic programming, finds the opt ..."
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Dynamic programming is introduced to quantize a continuous random variable into a discrete random variable. Quantization is often useful before statistical analysis or reconstruction of large network models among multiple random variables. The quantization, through dynamic programming, finds the optimal discrete representation of the original probability density function of a random variable by maximizing the likelihood for the observed data. This algorithm is highly applicable to study genomic features such as the recombination rate across the chromosomes and the statistical properties of noncoding elements such as LINE1. In particular, the recombination rate obtained by quantization is studied for LINE1 elements that are grouped also using quantization by length. The exact and densitypreserving quantization approach provides an alternative superior to the inexact and distancebased kmeans clustering algorithm for discretization of a single variable. 1