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31
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 125 (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.
Beyond Independence: Probabilistic Models for Query Approximation on Binary Transaction Data
, 2001
"... We investigate the problem of generating fast approximate answers to queries for large sparse binary data sets. We focus in particular on probabilistic modelbased approaches to this problem and develop a number of techniques that are significantly more accurate than a baseline independence model. I ..."
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Cited by 48 (6 self)
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We investigate the problem of generating fast approximate answers to queries for large sparse binary data sets. We focus in particular on probabilistic modelbased approaches to this problem and develop a number of techniques that are significantly more accurate than a baseline independence model. In particular, we introduce a novel technique for building probabilistic models from frequent itemsets. The itemsets are treated as constraints on the distribution of the query variables and the maximum entropy principle is used online to build a joint probability model for attributes in the query. We show that the resulting probability model defines a Markov random field (MRF) and that the time taken to answer a query scales exponentially as a function of the induced width of the associated MRF graph. We empirically compare the MRF model to other probabilistic models, such as the independence model, the ChowLiu tree model, the Bernoulli mixture model, and the ADTree model. Experimental resu...
Partial Correlation Estimation by Joint Sparse Regression Models
 JASA
, 2008
"... In this article, we propose a computationally efficient approach—space (Sparse PArtial Correlation Estimation)—for selecting nonzero partial correlations under the highdimensionlowsamplesize setting. This method assumes the overall sparsity of the partial correlation matrix and employs sparse re ..."
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Cited by 38 (4 self)
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In this article, we propose a computationally efficient approach—space (Sparse PArtial Correlation Estimation)—for selecting nonzero partial correlations under the highdimensionlowsamplesize setting. This method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting. We illustrate the performance of space by extensive simulation studies. It is shown that space performs well in both nonzero partial correlation selection and the identification of hub variables, and also outperforms two existing methods. We then apply space to a microarray breast cancer dataset and identify a set of hub genes that may provide important insights on genetic regulatory networks. Finally, we prove that, under a set of suitable assumptions, the proposed procedure is asymptotically consistent in terms of model selection and parameter estimation.
LASSOPatternsearch Algorithm with Application to Ophthalmology and Genomic Data
, 2008
"... The LASSOPatternsearch algorithm is proposed to efficiently identify patterns of multiple dichotomous risk factors for outcomes of interest in demographic and genomic studies. The patterns considered are those that arise naturally from the log linear expansion of the multivariate Bernoulli density. ..."
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Cited by 29 (22 self)
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The LASSOPatternsearch algorithm is proposed to efficiently identify patterns of multiple dichotomous risk factors for outcomes of interest in demographic and genomic studies. The patterns considered are those that arise naturally from the log linear expansion of the multivariate Bernoulli density. The method is designed for the case where there is a possibly very large number of candidate patterns but it is believed that only a relatively small number are important. A LASSO is used to greatly reduce the number of candidate patterns, using a novel computational algorithm that can handle an extremely large number of unknowns simultaneously. The patterns surviving the LASSO are further pruned in the framework of (parametric) generalized linear models. A novel tuning procedure based on the GACV for Bernoulli outcomes, modified to act
Remarks concerning graphical models for time series and point processes
 Revista de Econometria
, 1996
"... Uma rede estatística é uma cole,cão de nós representando variáveis aleatórias e um conjunto de arestas que ligam os nós. Um modelo estocástico por isso e chamado um modelo gráfico. Estes modelos, de gráficos e redes, sáo particularmente úteis para examinar as dependéncias estatísticas baseadas em co ..."
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Cited by 21 (3 self)
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Uma rede estatística é uma cole,cão de nós representando variáveis aleatórias e um conjunto de arestas que ligam os nós. Um modelo estocástico por isso e chamado um modelo gráfico. Estes modelos, de gráficos e redes, sáo particularmente úteis para examinar as dependéncias estatísticas baseadas em condi,coes do tipo das que ocorrem frequentemente em economia e estatística. Neste artigo as variáveis aleatórias dos nós serão séries temporais ou processos pontuais. Os casos de gráfos direcionados e nãodirecionados são apresentados. A statistical network is a collection of nodes representing random variables and a set of edges that connect the nodes. A probabilistic model for such is called a graphical model. These models, graphs and networks are particularly useful for examining statistical dependencies based on conditioning as often occurs in economics and statistics. In this paper the nodal random variables will be time series or point proceses. The cases of undirected and directed graphs are focussed on.
Spline adaptation in extended linear models
 Statistical Science
, 2002
"... Abstract. In many statistical applications, nonparametric modeling can provide insight into the features of a dataset that are not obtainable by other means. One successful approach involves the use of (univariate or multivariate) spline spaces. As a class, these methods have inherited much from cla ..."
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Cited by 16 (2 self)
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Abstract. In many statistical applications, nonparametric modeling can provide insight into the features of a dataset that are not obtainable by other means. One successful approach involves the use of (univariate or multivariate) spline spaces. As a class, these methods have inherited much from classical tools for parametric modeling. For example, stepwise variable selection with spline basis terms is a simple scheme for locating knots (breakpoints) in regions where the data exhibit strong, local features. Similarly, candidate knot con gurations (generated by this or some other search technique), are routinely evaluated with traditional selection criteria like AIC or BIC. In short, strategies typically applied in parametric model selection have proved useful in constructing exible, lowdimensional models for nonparametric problems. Until recently, greedy, stepwise procedures were most frequently suggested in the literature. Researchinto Bayesian variable selection, however, has given rise to a number of new splinebased methods that primarily rely on some form of Markov chain Monte Carlo to identify promising knot locations. In this paper, we consider various alternatives to greedy, deterministic schemes, and present aBayesian framework for studying adaptation in the context of an extended linear model (ELM). Our major test cases are Logspline density estimation and (bivariate) Triogram regression models. We selected these because they illustrate a number of computational and methodological issues concerning model adaptation that arise in ELMs.
Screening and interpreting multiitem associations based on loglinear modeling
 in KDD, 2003
"... Association rules have received a lot of attention in the data mining community since their introduction. The classical approach to find rules whose items enjoy high support (appear in a lot of the transactions in the data set) is, however, filled with shortcomings. It has been shown that support ca ..."
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Cited by 14 (8 self)
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Association rules have received a lot of attention in the data mining community since their introduction. The classical approach to find rules whose items enjoy high support (appear in a lot of the transactions in the data set) is, however, filled with shortcomings. It has been shown that support can be misleading as an indicator of how interesting the rule is. Alternative measures, such as lift, have been proposed. More recently, a paper by DuMouchel et al. proposed the use of alltwofactor loglinear models to discover sets of items that cannot be explained by pairwise associations between the items involved. This approach, however, has its limitations, since it stops short of considering higher order interactions (other than pairwise) among the items. In this paper, we propose a method that examines the parameters of the fitted loglinear models to find all the significant association patterns among the items. Since fitting loglinear models for large data sets can be computationally prohibitive, we apply graphtheoretical results to divide the original set of items into components (sets of items) that are statistically independent from each other. We then apply loglinear modeling to each of the components and find the interesting associations among items in them. The technique is experimentally evaluated with a real data set (insurance data) and a series of synthetic data sets. The results show that the technique is effective in finding interesting associations among the items involved.
Interactive Analysis of Gene Interactions Using Graphical Gaussian Model
 ACM SIGKDD Workshop on Data Mining in Bioinformatics, 3:63–69
, 2003
"... DNA microarray provides a powerful basis for analysis of gene expression. Data mining methods such as clustering have been widely applied to microarray data to link genes that show similar expression patterns. However, this approach usually fails to unveil genegene interactions in the same cluster. ..."
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Cited by 12 (0 self)
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DNA microarray provides a powerful basis for analysis of gene expression. Data mining methods such as clustering have been widely applied to microarray data to link genes that show similar expression patterns. However, this approach usually fails to unveil genegene interactions in the same cluster. Association rule mining and loglinear models have been used for this purpose, but their inherent limitations as well as information loss due to discretization limit the applicability of the results. Here we propose the use of a Graphical Gaussian Model to discover pairwise gene interactions. We have constructed a prototype system that permits rapid interactive exploration of gene relationships; results can be validated by experts or known information, or suggest new experiments. We have tested our methodology using the yeast microarray data. Our results reveal some previously unknown interactions that have solid biological explanations.
RealTime Distributed MultiObject Tracking Using Multiple Interactive Trackers and a MagneticInertia Potential Model
"... Abstract—This paper presents a method which avoids the common practice of using a complex joint statespace representation and performing tedious joint data association for multiple object tracking applications. Instead, we propose a distributed Bayesian formulation using multiple interactive tracke ..."
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Cited by 9 (2 self)
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Abstract—This paper presents a method which avoids the common practice of using a complex joint statespace representation and performing tedious joint data association for multiple object tracking applications. Instead, we propose a distributed Bayesian formulation using multiple interactive trackers that requires much lower complexity for realtime tracking applications. When the objects ’ observations do not interact with each other, our approach performs as multiple independent trackers. However, when the objects ’ observations exhibit interaction, defined as close proximity or partial and complete occlusion, we extend the conventional Bayesian tracking framework by modeling such interaction in terms of potential functions. The proposed “magneticinertia” model represents the cumulative effect of virtual physical forces that objects undergo while interacting with each other. It implicitly handles the “error merge ” and “object labeling” problems and thus solves the difficult object occlusion and data association problems in an innovative way. Our preliminary simulations have demonstrated that the proposed approach is far superior to other methods in both robustness and speed. Index Terms—Bayesian tracking, data association, multiple object tracking, object occlusion, particle filter. I.
MAMBO: Discovering Association Rules Based on Conditional Independencies
 LNCS
, 2001
"... We present the Mambo algorithm for the discovery of association rules. Mambo is driven by conditional independence relations between the variables instead of the minimum support restrictions of algorithms like Apriori. We argue that making use of conditional independencies is an intuitively appealin ..."
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Cited by 8 (2 self)
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We present the Mambo algorithm for the discovery of association rules. Mambo is driven by conditional independence relations between the variables instead of the minimum support restrictions of algorithms like Apriori. We argue that making use of conditional independencies is an intuitively appealing way to restrict the set of association rules considered. Since we only have a finite sample from the probability distribution of interest, we have to deal with uncertainty concerning the conditional independencies present. Bayesian methods are used to quantify this uncertainty, and the posterior probabilities of conditional independence relations are estimated with the Markov Chain Monte Carlo technique. We analyse an insurance data set with Mambo and illustrate the differences in results compared to Apriori.