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Iterative conditional fitting for discrete chain graph models
 In COMPSTAT 2008 – Proceedings in Computational Statistics 93–104
, 2008
"... Abstract. ‘Iterative conditional fitting ’ is a recently proposed algorithm that can be used for maximization of the likelihood function in marginal independence models for categorical data. This paper describes a modification of this algorithm, which allows one to compute maximum likelihood estimat ..."
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Abstract. ‘Iterative conditional fitting ’ is a recently proposed algorithm that can be used for maximization of the likelihood function in marginal independence models for categorical data. This paper describes a modification of this algorithm, which allows one to compute maximum likelihood estimates in a class of chain graph models for categorical data. The considered discrete chain graph models are defined using conditional independence relations arising in recursive multivariate regressions with correlated errors. This Markov interpretation of the chain graph is consistent with treating the graph as a path diagram and differs from other interpretations known as the LWF and AMP Markov properties.
Modelling Relational Statistics With Bayes Nets
"... Abstract. Classlevel models capture relational statistics over object attributes and their connecting links, answering questions such as “what is the percentage of friendship pairs where both friends are women?” Classlevel relationships are important in themselves, and they support applications li ..."
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Abstract. Classlevel models capture relational statistics over object attributes and their connecting links, answering questions such as “what is the percentage of friendship pairs where both friends are women?” Classlevel relationships are important in themselves, and they support applications like policy making, strategic planning, and query optimization. We represent class statistics using Parametrized Bayes Nets (PBNs), a firstorder logic extension of Bayes nets. Queries about classes require a new semantics for PBNs, as the standard grounding semantics is only appropriate for answering queries about specific ground facts. We propose a novel random selection semantics for PBNs, which does not make reference to a ground model, and supports classlevel queries. The parameters for this semantics can be learned using the recent pseudolikelihood measure [1] as the objective function. This objective function is maximized by taking the empirical frequencies in the relational data as the parameter settings. We render the computation of these empirical frequencies tractable in the presence of negated relations by the inverse Möbius transform. Evaluation of our method on four benchmark datasets shows that maximum pseudolikelihood provides fast and accurate estimates at different sample sizes. 1
Independence in MultiWay Contingency Tables: S. N. Roy’s Breakthroughs and Later Developments
"... contingency tables: ..."
1 Philosophy Research Statement
, 2006
"... My work lies on the intersection of computer science and statistics. The questions I want to answer are of the following nature: how can machines learn from experience? This raises questions about statistical modeling, since the nature of a phenomenon is only observable through a limited set of meas ..."
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My work lies on the intersection of computer science and statistics. The questions I want to answer are of the following nature: how can machines learn from experience? This raises questions about statistical modeling, since the nature of a phenomenon is only observable through a limited set of measurements: the data. Rather than explicitly programming a computer to perform a particular task, machine learning uses data and statistical models to achieve intelligent behavior. The outcome can be observed in tasks as diverse as: predicting user preferences (movie ratings are fashionable these days 1); filtering spam; adapting models of computer vision and speech recognition to new environments; improving retrieval of important documents; improving machine translation; and many others. We can also turn the question around and ask instead how machines can be used in new methods of data analysis, and improve scientific progress. Standard statistical practice focuses on studies with a small number of variables and data points, but the increase in the amount of data that has been collected is evident. The need for analysing high dimensional measurements, and combining different sources of data, is pressing. Now the issue turns to finding proper computational approaches for building models from data, and providing novel techniques for exploration and analysis within more thorough studies. In particular, my research addresses fundamental questions on learning with graphical models. More
Bayesian Inference for Discrete Mixed Graph Models: Normit Networks, Observable Independencies and Infinite Mixtures
"... Directed mixed graphs are graphical representations that include directed and bidirected edges. Such a class is motivated by dependencies that arise when hidden common causes are marginalized out of a distribution. In previous work, we introduced an efficient Monte Carlo algorithm for sampling from ..."
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Directed mixed graphs are graphical representations that include directed and bidirected edges. Such a class is motivated by dependencies that arise when hidden common causes are marginalized out of a distribution. In previous work, we introduced an efficient Monte Carlo algorithm for sampling from Gaussian mixed graph models. An analogous model for discrete distributions is likely to be doublyintractable, in the sense that even a single Markov Chain Monte Carlo step might have a computational cost that scales exponentially with the number of variables. Instead, we built upon our results on Gaussian distributions to describe algorithms and priors for discrete binary and ordinal modeling. The models we describe are based on link functions, where a multivariate Gaussian distribution encoded by a mixed graph is projected into a discrete space. In order to account for flexible discrete distributions, we embed this model within a Dirichlet process mixture of Gaussians. 1