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Locationbased activity recognition
 In Advances in Neural Information Processing Systems (NIPS
, 2005
"... Learning patterns of human behavior from sensor data is extremely important for highlevel activity inference. We show how to extract and label a person’s activities and significant places from traces of GPS data. In contrast to existing techniques, our approach simultaneously detects and classifies ..."
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Cited by 54 (6 self)
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Learning patterns of human behavior from sensor data is extremely important for highlevel activity inference. We show how to extract and label a person’s activities and significant places from traces of GPS data. In contrast to existing techniques, our approach simultaneously detects and classifies the significant locations of a person and takes the highlevel context into account. Our system uses relational Markov networks to represent the hierarchical activity model that encodes the complex relations among GPS readings, activities and significant places. We apply FFTbased message passing to perform efficient summation over large numbers of nodes in the networks. We present experiments that show significant improvements over existing techniques. 1
Binary models for marginal independence
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B
, 2005
"... A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Möbius inversion and maximum likelihood estimation can be performed using a versi ..."
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Cited by 16 (2 self)
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A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Möbius inversion and maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. The approach is illustrated on a simple example. Relations to multivariate logistic and dependence ratio models are discussed.
Cumulative distribution networks and the derivativesumproduct algorithm
"... We introduce a new type of graphical model called a ‘cumulative distribution network’ (CDN), which expresses a joint cumulative distribution as a product of local functions. Each local function can be viewed as providing evidence about possible orderings, or rankings, of variables. Interestingly, we ..."
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Cited by 12 (6 self)
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We introduce a new type of graphical model called a ‘cumulative distribution network’ (CDN), which expresses a joint cumulative distribution as a product of local functions. Each local function can be viewed as providing evidence about possible orderings, or rankings, of variables. Interestingly, we find that the conditional independence properties of CDNs are quite different from other graphical models. We also describe a messagepassing algorithm that efficiently computes conditional cumulative distributions. Due to the unique independence properties of the CDN, these messages do not in general have a onetoone correspondence with messages exchanged in standard algorithms, such as belief propagation. We demonstrate the application of CDNs for structured ranking learning using a previouslystudied multiplayer gaming dataset. 1
Graphical methods for efficient likelihood inference in gaussian covariance models
 Journal of Machine Learning
, 2008
"... Abstract. In graphical modelling, a bidirected graph encodes marginal independences among random variables that are identified with the vertices of the graph. We show how to transform a bidirected graph into a maximal ancestral graph that (i) represents the same independence structure as the origi ..."
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Cited by 8 (3 self)
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Abstract. In graphical modelling, a bidirected graph encodes marginal independences among random variables that are identified with the vertices of the graph. We show how to transform a bidirected graph into a maximal ancestral graph that (i) represents the same independence structure as the original bidirected graph, and (ii) minimizes the number of arrowheads among all ancestral graphs satisfying (i). Here the number of arrowheads of an ancestral graph is the number of directed edges plus twice the number of bidirected edges. In Gaussian models, this construction can be used for more efficient iterative maximization of the likelihood function and to determine when maximum likelihood estimates are equal to empirical counterparts. 1.
On factor graphs and the Fourier transform
 In IEEE Trans. Inform. Theory
, 2005
"... Abstract—We introduce the concept of convolutional factor graphs, which represent convolutional factorizations of multivariate functions, just as conventional (multiplicative) factor graphs represent multiplicative factorizations. Convolutional and multiplicative factor graphs arise as natural Fouri ..."
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Cited by 7 (1 self)
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Abstract—We introduce the concept of convolutional factor graphs, which represent convolutional factorizations of multivariate functions, just as conventional (multiplicative) factor graphs represent multiplicative factorizations. Convolutional and multiplicative factor graphs arise as natural Fourier transform duals. In coding theory applications, algebraic duality of group codes is essentially an instance of Fourier transform duality. Convolutional factor graphs arise when a code is represented as a sum of subcodes, just as conventional multiplicative factor graphs arise when a code is represented as an intersection of supercodes. With auxiliary variables, convolutional factor graphs give rise to “syndrome realizations ” of codes, just as multiplicative factor graphs with auxiliary variables give rise to “state realizations.” We introduce normal and conormal extensions of a multivariate function, which essentially allow a given function to be represented with either a multiplicative or a convolutional factorization, as is convenient. We use these function extensions to derive a number of duality relationships among the corresponding factor graphs, and use these relationships to obtain the duality properties of Forney graphs as a special case. Index Terms—Duality, factor graphs, Forney graphs, Fourier transform, graphical models, normal realizations, state realizations, syndrome realizations, Tanner graphs. I.
Hybrid Bayesian networks with linear deterministic variables, in
 F. Bacchus, T. Jaakkola (Eds.), Uncertainty in Artificial Intelligence
, 2005
"... When a hybrid Bayesian network has conditionally deterministic variables with continuous parents, the joint density function for the continuous variables does not exist. Conditional linear Gaussian distributions can handle such cases when the continuous variables have a multivariate normal distribu ..."
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Cited by 2 (1 self)
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When a hybrid Bayesian network has conditionally deterministic variables with continuous parents, the joint density function for the continuous variables does not exist. Conditional linear Gaussian distributions can handle such cases when the continuous variables have a multivariate normal distribution and the discrete variables do not have continuous parents. In this paper, operations required for performing inference with conditionally deterministic variables in hybrid Bayesian networks are developed. These methods allow inference in networks with deterministic variables where continuous variables may be nonGaussian, and their density functions can be approximated by mixtures of truncated exponentials. There are no constraints on the placement of continuous and discrete nodes in the network. 1
J.A.: Nonminimal triangulations for mixed stochastic/deterministic graphical models
 In: Proceedings of the Twenty Second Conference on Uncertainty in Artificial Intelligence (UAI’06
, 2006
"... We observe that certain largeclique graph triangulations can be useful for reducing computational requirements when making queries on mixed stochastic/deterministic graphical models. We demonstrate that many of these largeclique triangulations are nonminimal and are thus unattainable via the elimi ..."
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Cited by 2 (1 self)
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We observe that certain largeclique graph triangulations can be useful for reducing computational requirements when making queries on mixed stochastic/deterministic graphical models. We demonstrate that many of these largeclique triangulations are nonminimal and are thus unattainable via the elimination algorithm. We introduce ancestral pairs as the basis for novel triangulation heuristics and prove that no more than the addition of edges between ancestral pairs need be considered when searching for state space optimal triangulations in such graphs. Empirical results on random and real world graphs are given. We also present an algorithm and correctness proof for determining if a triangulation can be obtained via elimination, and we show that the decision problem associated with finding optimal state space triangulations in this mixed setting is NPcomplete. 1
Inference with Multivariate HeavyTails in Linear Models
"... Heavytailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closedform in graphical models which involve such heavytailed distributions. In this work, we propose a novel simple linear graphical model for independent lat ..."
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Cited by 1 (0 self)
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Heavytailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closedform in graphical models which involve such heavytailed distributions. In this work, we propose a novel simple linear graphical model for independent latent random variables, called linear characteristic model (LCM), defined in the characteristic function domain. Using stable distributions, a heavytailed family of distributions which is a generalization of Cauchy, Lévy and Gaussian distributions, we show for the first time, how to compute both exact and approximate inference in such a linear multivariate graphical model. LCMs are not limited to stable distributions, in fact LCMs are always defined for any random variables (discrete, continuous or a mixture of both). We provide a realistic problem from the field of computer networks to demonstrate the applicability of our construction. Other potential application is iterative decoding of linear channels with nonGaussian noise. 1
Graphical Answers to . . .
, 2004
"... In graphical modelling, a bidirected graph encodes marginal independences among random variables that are identified with the vertices of the graph (alternatively graphs with dashed edges have been used for this purpose). Bidirected graphs are special instances of ancestral graphs, which are mixed ..."
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In graphical modelling, a bidirected graph encodes marginal independences among random variables that are identified with the vertices of the graph (alternatively graphs with dashed edges have been used for this purpose). Bidirected graphs are special instances of ancestral graphs, which are mixed graphs with undirected, directed, and bidirected edges. In this paper, we show how simplicial sets and the newly defined orientable edges can be used to construct a maximal ancestral graph that is Markov equivalent to a given bidirected graph, i.e. the independence models associated with the two graphs coincide, and such that the number of arrowheads is minimal. Here the number of arrowheads of an ancestral graph is the number of directed edges plus twice the number of bidirected edges. This construction yields an immediate check whether the original bidirected graph is Markov equivalent to a directed acyclic graph (Bayesian network) or an undirected graph (Markov random field). Moreover, the ancestral graph construction allows for computationally more efficient maximum likelihood fitting of covariance graph models, i.e. Gaussian bidirected graph models. In particular, we give a necessary and sufficient graphical criterion for determining when an entry of the maximum likelihood estimate of the covariance matrix must equal its empirical counterpart.