McGill Statistics Seminar

Date: 2012-01-20

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Latent variable mixture models are a powerful tool for exploring the structure in large datasets. A common challenge for interpreting such models is a desire to impose sparsity, the natural assumption that each data point only contains few latent features. Since mixture distributions are constrained in their L1 norm, typical sparsity techniques based on L1 regularization become toothless, and concave regularization becomes necessary. Unfortunately concave regularization typically results in EM algorithms that must perform problematic non-convex M-step optimization. In this work, we introduce a technique for circumventing this difficulty, using the so-called Mountain Pass Theorem to provide easily verifiable conditions under which the M-step is well-behaved despite the lacking convexity. We also develop a correspondence between logarithmic regularization and what we term the pseudo-Dirichlet distribution, a generalization of the ordinary Dirichlet distribution well-suited for inducing sparsity. We demonstrate our approach on a text corpus, inferring a sparse topic mixture model for 2,406 weblogs.

Date: 2011-12-02

Time: 15:30-16:30

Location: BURN 1205

Abstract:

This talk focuses on the problem of the estimation of a distribution on an arbitrary complete separable metric space when the data points are subject to censoring by a general class of random sets. A path-dependent estimator for the distribution is proposed; among other properties, the estimator is sequential in the sense that it only uses data preceding any fixed point at which it is evaluated. If the censoring mechanism is totally ordered, the paths may be chosen in such a way that the estimate of the distribution defines a measure. In this case, we can prove a functional central limit theorem for the estimator when the underlying space is Euclidean. This is joint work with Gail Ivanoff (University of Ottawa)

Date: 2011-11-25

Time: 15:30-16:30

Location: BURN 1205

Abstract:

The use of cell phone while driving raises the question of whether it is associated with an increased collision risk and if so, what is its magnitude. For policy decision making, it is important to rely on an accurate estimate of the real crash risk of cell phone use while driving. Three important epidemiological studies were published on the subject, two using the case-crossover approach and one using a more conventional longitudinal cohort design. The methodology and results of these studies will be presented and discussed.

Date: 2011-11-18

Time: 15:30-16:30

Location: BURN 1205

Abstract:

The diagonal expansion of a bivariate distribution (Lancaster, 1958) has been used as a tool to construct bivariate distributions; this method has been generalized using principal dimensions of random variables (Cuadras 2002). Sufficient and necessary conditions are given for uniform, exponential, logistic and Pareto marginals in the one and two-dimensional case. The corresponding copulas are obtained.

Speaker

Amparo Casanova is an Assistant Professor at the Dalla Lana School of Public Health, Division of Biostatistics, University of Toronto.

Date: 2011-11-04

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Diffusion processes have been used to model a multitude of continuous-time phenomena in Engineering and the Natural Sciences, and as in this case, the volatility of financial assets. However, parametric inference has long been complicated by an intractable likelihood function. For many models the most effective solution involves a large amount of missing data for which the typical Gibbs sampler can be arbitrarily slow. On the other hand, joint parameter and missing data proposals can lead to a radical improvement, but their acceptance rate tends to scale exponentially with the number of observations.

Date: 2011-11-03

Time: 16:00-17:00

Location: BURN 1205

Abstract:

This talk is concerned with maximum likelihood estimation (MLE) in exponential statistical models for networks (random graphs) and, in particular, with the beta model, a simple model for undirected graphs in which the degree sequence is the minimal sufficient statistic. The speaker will present necessary and sufficient conditions for the existence of the MLE of the beta model parameters that are based on a geometric object known as the polytope of degree sequences. Using this result, it is possible to characterize in a combinatorial fashion sample points leading to a non-existent MLE and non-estimability of the probability parameters under a non-existent MLE. The speaker will further indicate some conditions guaranteeing that the MLE exists with probability tending to 1 as the number of nodes increases. Much of this analysis applies also to other well-known models for networks, such as the Rasch model, the Bradley-Terry model and the more general p1 model of Holland and Leinhardt. These results are in fact instantiations of rather general geometric properties of exponential families with polyhedral support that will be illustrated with a simple exponential random graph model.

Date: 2011-10-28

Time: 15:00-16:00

Location: BURN 1205

Abstract:

This paper considers the estimation of the parameters of a copula via a simulated method of moments type approach. This approach is attractive when the likelihood of the copula model is not known in closed form, or when the researcher has a set of dependence measures or other functionals of the copula, such as pricing errors, that are of particular interest. The proposed approach naturally also nests method of moments and generalized method of moments estimators. Combining existing results on simulation based estimation with recent results from empirical copula process theory, we show the consistency and asymptotic normality of the proposed estimator, and obtain a simple test of over-identifying restrictions as a goodness-of-fit test. The results apply to both iid and time series data. We analyze the finite-sample behavior of these estimators in an extensive simulation study. We apply the model to a group of seven financial stock returns and find evidence of statistically significant tail dependence, and that the dependence between these assets is stronger in crashes than booms.

Date: 2011-10-21

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Genome-wide association studies (GWAS) are used to identify physical positions (loci) on the genome where genetic variation is causally associated with a phenotype of interest at the population level. Typical studies are based on the measurement of several hundred thousand single nucleotide polymorphism (SNP) variants spread across the genome, in a few thousand individuals. The resulting datasets are large and require computationally efficient methods of statistical analysis.

Date: 2011-10-07

Time: 15:30-16:30

Location: BURN 1205

Abstract:

In this talk, the following topics will be discussed: A class of bivariate probability integral transforms and Kendall distribution; bivariate quantile curves, central and lateral regions; non-exchangeability and radial asymmetry identification; new measures of nonexchangeability and radial asymmetry; financial applications and a few open problems (joint work with Flavio Ferreira).

Speaker

Nikolai Kolev is a Professor of Statistics at the University of Sao Paulo, Brazil.

Date: 2011-09-30

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Streaming data is ubiquitous in a wide range of areas from engineering and information technology, finance, and commerce, to atmospheric physics, and earth sciences. The online approximation of properties of data streams is of great interest, but this approximation process is hindered by the sheer size of the data and the speed at which it is generated. Data stream algorithms typically allow only one pass over the data, and maintain sub-linear representations of the data from which target properties can be inferred with high efficiency.