Marginals of DAG-Isomorphic Independence Models

Probabilistic and graphical independence models both satisfy the semi-graphoid axioms, but their respective modelling powers are not equal. For every graphical independence model that is represented by d-separation in a directed acyclic graph, there exists an isomorphic probabilistic independence model, i.e. it has exactly the same independence statements. The reverse does not hold, as there exist probability distributions for which there are no perfect maps. We investigate if a given probabilistic independence model can be augmented with latent variables to a new independence model that is isomorphic with a graphical independence model of a directed acyclic graph. The original independence model can then be viewed as the marginal of the model with latent variables. We show that for some independence models we need infinitely many latent variables to accomplish this

Sufficient Covariate, Propensity Variable and Doubly Robust Estimation

Statistical causal inference from observational studies often requires adjustment for a possibly multi-dimensional variable, where dimension reduction is crucial. The propensity score, first introduced by Rosenbaum and Rubin, is a popular approach to such reduction. We address causal inference within Dawid's decision-theoretic framework, where it is essential to pay attention to sufficient covariates and their properties. We examine the role of a propensity variable in a normal linear model. We investigate both population-based and sample-based linear regressions, with adjustments for a multivariate covariate and for a propensity variable. In addition, we study the augmented inverse probability weighted estimator, involving a combination of a response model and a propensity model. In a linear regression with homoscedasticity, a propensity variable is proved to provide the same estimated causal effect as multivariate adjustment. An estimated propensity variable may, but need not, yield better precision than the true propensity variable. The augmented inverse probability weighted estimator is doubly robust and can improve precision if the propensity model is correctly specified

Leading strategies in competitive on-line prediction

We start from a simple asymptotic result for the problem of on-line regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a "leading prediction strategy", which not only asymptotically performs at least as well as any continuous limited-memory strategy but also satisfies the property that the excess loss of any continuous limited-memory strategy is determined by how closely it imitates the leading strategy. More specifically, for any class of prediction strategies constituting a reproducing kernel Hilbert space we construct a leading strategy, in the sense that the loss of any prediction strategy whose norm is not too large is determined by how closely it imitates the leading strategy. This result is extended to the loss functions given by Bregman divergences and by strictly proper scoring rules.Comment: 20 pages; a conference version is to appear in the ALT'2006 proceeding

Dynamic Bayesian Combination of Multiple Imperfect Classifiers

Classifier combination methods need to make best use of the outputs of multiple, imperfect classifiers to enable higher accuracy classifications. In many situations, such as when human decisions need to be combined, the base decisions can vary enormously in reliability. A Bayesian approach to such uncertain combination allows us to infer the differences in performance between individuals and to incorporate any available prior knowledge about their abilities when training data is sparse. In this paper we explore Bayesian classifier combination, using the computationally efficient framework of variational Bayesian inference. We apply the approach to real data from a large citizen science project, Galaxy Zoo Supernovae, and show that our method far outperforms other established approaches to imperfect decision combination. We go on to analyse the putative community structure of the decision makers, based on their inferred decision making strategies, and show that natural groupings are formed. Finally we present a dynamic Bayesian classifier combination approach and investigate the changes in base classifier performance over time.Comment: 35 pages, 12 figure

Nonparametric Information Geometry

The differential-geometric structure of the set of positive densities on a given measure space has raised the interest of many mathematicians after the discovery by C.R. Rao of the geometric meaning of the Fisher information. Most of the research is focused on parametric statistical models. In series of papers by author and coworkers a particular version of the nonparametric case has been discussed. It consists of a minimalistic structure modeled according the theory of exponential families: given a reference density other densities are represented by the centered log likelihood which is an element of an Orlicz space. This mappings give a system of charts of a Banach manifold. It has been observed that, while the construction is natural, the practical applicability is limited by the technical difficulty to deal with such a class of Banach spaces. It has been suggested recently to replace the exponential function with other functions with similar behavior but polynomial growth at infinity in order to obtain more tractable Banach spaces, e.g. Hilbert spaces. We give first a review of our theory with special emphasis on the specific issues of the infinite dimensional setting. In a second part we discuss two specific topics, differential equations and the metric connection. The position of this line of research with respect to other approaches is briefly discussed.Comment: Submitted for publication in the Proceedings od GSI2013 Aug 28-30 2013 Pari

A new determination of the orbit and masses of the Be binary system delta Scorpii

The binary star delta Sco (HD143275) underwent remarkable brightening in the visible in 2000, and continues to be irregularly variable. The system was observed with the Sydney University Stellar Interferometer (SUSI) in 1999, 2000, 2001, 2006 and 2007. The 1999 observations were consistent with predictions based on the previously published orbital elements. The subsequent observations can only be explained by assuming that an optically bright emission region with an angular size of > 2 +/- 1 mas formed around the primary in 2000. By 2006/2007 the size of this region grew to an estimated > 4 mas. We have determined a consistent set of orbital elements by simultaneously fitting all the published interferometric and spectroscopic data as well as the SUSI data reported here. The resulting elements and the brightness ratio for the system measured prior to the outburst in 2000 have been used to estimate the masses of the components. We find Ma = 15 +/- 7 Msun and Mb = 8.0 +/- 3.6 Msun. The dynamical parallax is estimated to be 7.03 +/- 0.15 mas, which is in good agreement with the revised HIPPARCOS parallax.Comment: 8 pages, 4 figs. Accepted for publication in MNRA

Matrix-Variate Discriminative Analysis, Integrative Hypothesis Testing, and Geno-Pheno A5 Analyzer

Abstract. A general perspective is provided on both on hypothesis testing and discriminative analyses, by which matrix-variate discriminative analyses are pro-posed based on the matrix normal distribution, featured by a bi-linear extension of Fisher linear discriminant analysis and a further extension to binary variables. Moreover, a general formulation is proposed for integrative hypothesis testing and five typical categories are summarized. Furthermore, major techniques for varia-ble selection are briefly elaborated. Finally, taking analyses of gene expression and exome sequencing as examples, we further propose a general procedure called Geno-Pheno A5 Analyzer for integrative discriminant analysis