/post/index.xml Past Seminar Series - McGill Statistics Seminars

Past Seminar Series

  • Estimating high-dimensional multi-layered networks through penalized maximum likelihood

    George Michailidis · Oct 16, 2015

    Date: 2015-10-16

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Gaussian graphical models represent a good tool for capturing interactions between nodes represent the underlying random variables. However, in many applications in biology one is interested in modeling associations both between, as well as within molecular compartments (e.g., interactions between genes and proteins/metabolites). To this end, inferring multi-layered network structures from high-dimensional data provides insight into understanding the conditional relationships among nodes within layers, after adjusting for and quantifying the effects of nodes from other layers. We propose an integrated algorithmic approach for estimating multi-layered networks, that incorporates a screening step for significant variables, an optimization algorithm for estimating the key model parameters and a stability selection step for selecting the most stable effects. The proposed methodology offers an efficient way of estimating the edges within and across layers iteratively, by solving an optimization problem constructed based on penalized maximum likelihood (under a Gaussianity assumption). The optimization is solved on a reduced parameter space that is identified through screening, which remedies the instability in high-dimension. Theoretical properties are considered to ensure identifiability and consistent estimation of the parameters and convergence of the optimization algorithm, despite the lack of global convexity. The performance of the methodology is illustrated on synthetic data sets and on an application on gene and metabolic expression data for patients with renal disease.

  • Parameter estimation of partial differential equations over irregular domains

    Michelle Carey · Oct 9, 2015

    Date: 2015-10-09

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Spatio-temporal data are abundant in many scientific fields; examples include daily satellite images of the earth, hourly temperature readings from multiple weather stations, and the spread of an infectious disease over a particular region. In many instances the spatio-temporal data are accompanied by mathematical models expressed in terms of partial differential equations (PDEs). These PDEs determine the theoretical aspects of the behavior of the physical, chemical or biological phenomena considered. Azzimonti (2013) showed that including the associated PDE as a regularization term as opposed to the conventional two-dimensional Laplacian provides a considerable improvement in the estimation accuracy. The PDEs parameters often have interesting interpretations. Although they are typically unknown and must be inferred from expert knowledge of the phenomena considered. In this talk I will discuss extending the profiling with a parameter cascading procedure outlined in Ramsay et al. (2007) to incorporate PDE parameter estimation. I will also show how, following Sangalli et al. (2013), the estimation procedure can be extended to include finite-element methods (FEMs). This allows the proposed method to account for attributes of the geometry of the physical problem such as irregular shaped domains, external and internal boundary features, as well as strong concavities. Thus this talk will introduce a methodology for data-driven estimates of the parameters of PDEs defined over irregular domains.

  • Estimating covariance matrices of intermediate size

    Didier Chételat · Oct 2, 2015

    Date: 2015-10-02

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    In finance, the covariance matrix of many assets is a key component of financial portfolio optimization and is usually estimated from historical data. Much research in the past decade has focused on improving estimation by studying the asymptotics of large covariance matrices in the so-called high-dimensional regime, where the dimension p grows at the same pace as the sample size n, and this approach has been very successful. This choice of growth makes sense in part because, based on results for eigenvalues, it appears that there are only two limits: the high-dimensional one when p grows like n, and the classical one, when p grows more slowly than n. In this talk, I will present evidence that this binary view is false, and that there could be hidden intermediate regimes lying in between. In turn, this allows for corrections to the sample covariance matrix that are more appropriate when the dimension is large but moderate with respect to the sample size, as is often the case; this can also lead to better optimization for portfolio volatility in many situations of interest.

  • Topics in statistical inference for the semiparametric elliptical copula model

    Yue Zhao · Sep 25, 2015

    Date: 2015-09-25

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    This talk addresses aspects of the statistical inference problem for the semiparametric elliptical copula model. The semiparametric elliptical copula model is the family of distributions whose dependence structures are specified by parametric elliptical copulas but whose marginal distributions are left unspecified. An elliptical copula is uniquely characterized by a characteristic generator and a copula correlation matrix Sigma. In the first part of this talk, I will consider the estimation of Sigma. A natural estimate for Sigma is the plug-in estimator Sigmahat with Kendall’s tau statistic. I will first exhibit a sharp bound on the operator norm of Sigmahat - Sigma. I will then consider a factor model of Sigma, for which I will propose a refined estimator Sigmatilde by fitting a low-rank matrix plus a diagonal matrix to Sigmahat using least squares with a nuclear norm penalty on the low-rank matrix. The bound on the operator norm of Sigmahat - Sigma serves to scale the penalty term, and we obtained finite-sample oracle inequalities for Sigmatilde that I will present. In the second part of this talk, we will look at the classification of two distributions that have the same Gaussian copula but that are otherwise arbitrary in high dimensions. Under this semiparametric Gaussian copula setting, I will give an accurate semiparametric estimator of the log-density ratio, which leads to an empirical decision rule and a bound on its associated excess risk. Our estimation procedure takes advantage of the potential sparsity as well as the low noise condition in the problem, which allows us to achieve faster convergence rate of the excess risk than is possible in the existing literature on semiparametric Gaussian copula classification. I will demonstrate the efficiency of our semiparametric empirical decision rule by showing that the bound on the excess risk nearly achieves a convergence rate of 1 over square-root-n in the simple setting of Gaussian distribution classification.

  • A unified algorithm for fitting penalized models with high-dimensional data

    Yi Yang · Sep 18, 2015

    Date: 2015-09-18

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    In the light of high-dimensional problems, research on the penalized model has received much interest. Correspondingly, several algorithms have been developed for solving penalized high-dimensional models. I will describe fast and efficient unified algorithms for computing the solution path for a collection of penalized models. In particular, we will look at an algorithm for solving L1-penalized learning problems and an algorithm for solving group-lasso learning problems. These algorithm take advantage of a majorization-minimization trick to make each update simple and efficient. The algorithms also enjoy a proven convergence property. To demonstrate the generality of these algorithms, I extend them to a class of elastic net penalized large margin classification methods and to elastic net penalized Cox proportional hazards models. These algorithms have been implemented in three R packages gglasso, gcdnet and fastcox, which are publicly available from the Comprehensive R Archive Network (CRAN) at http://cran.r-project.org/web/packages. On simulated and real data, our algorithms consistently outperform the existing software in speed for computing penalized models and often delivers better quality solutions.

  • Bias correction in multivariate extremes

    Anne-Laure Fougères · Sep 11, 2015

    Date: 2015-09-11

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    The estimation of the extremal dependence structure of a multivariate extreme-value distribution is spoiled by the impact of the bias, which increases with the number of observations used for the estimation. Already known in the univariate setting, the bias correction procedure is studied in this talk under the multivariate framework. New families of estimators of the stable tail dependence function are obtained. They are asymptotically unbiased versions of the empirical estimator introduced by Huang (1992). Given that the new estimators have a regular behavior with respect to the number of observations, it is possible to deduce aggregated versions so that the choice of threshold is substantially simplified. An extensive simulation study is provided as well as an application on real data.

  • Some new classes of bivariate distributions based on conditional specification

    José María Sarabia · May 14, 2015

    Date: 2015-05-14

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    A bivariate distribution can sometimes be characterized completely by properties of its conditional distributions. In this talk, we will discuss models of bivariate distributions whose conditionals are members of prescribed parametric families of distributions. Some relevant models with specified conditionals will be discussed, including the normal and lognormal cases, the skew-normal and other families of distributions. Finally, some conditionally specified densities will be shown to provide convenient flexible conjugate prior families in certain multiparameter Bayesian settings.

  • A statistical view of some recent climate controversies

    Robert Lund · May 7, 2015

    Date: 2015-05-07

    Time: 15:30-16:30

    Location: Université de Sherbrooke

    Abstract:

    This talk looks at some recent climate controversies from a statistical standpoint. The issues are motivated via changepoints and their detection. Changepoints are ubiquitous features in climatic time series, occurring whenever stations relocate or gauges are changed. Ignoring changepoints can produce spurious trend conclusions. Changepoint tests involving cumulative sums, likelihood ratio, and maximums of F-statistics are introduced; the asymptotic distributions of these statistics are quantified under the changepoint-free null hypothesis. The case of multiple changepoints is considered. The methods are used to study several controversies, including extreme temperature trends in the United States and Atlantic Basin tropical cyclone counts and strengths.

  • Testing for network community structure

    Beate Franke · Mar 20, 2015

    Date: 2015-03-20

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Networks provide a useful means to summarize sparse yet structured massive datasets, and so are an important aspect of the theory of big data. A key question in this setting is to test for the significance of community structure or what in social networks is termed homophily, the tendency of nodes to be connected based on similar characteristics. Network models where a single parameter per node governs the propensity of connection are popular in practice, because they are simple to understand and analyze. They frequently arise as null models to indicate a lack of community structure, since they cannot readily describe the division of a network into groups of nodes whose aggregate links behave in a block-like manner. Here we discuss asymptotic regimes under families of such models, and show their potential for enabling hypothesis tests in this setting. As an important special case, we treat network modularity, which summarizes the difference between observed and expected within-community edges under such null models, and which has seen much success in practical applications of large-scale network analysis. Our focus here is on statistical rather than algorithmic properties, however, in order to yield new insights into the canonical problem of testing for network community structure.

  • Bayesian approaches to causal inference: A lack-of-success story

    David A. Stephens · Mar 13, 2015

    Date: 2015-03-13

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Despite almost universal acceptance across most fields of statistics, Bayesian inferential methods have yet to breakthrough to widespread use in causal inference, despite Bayesian arguments being a core component of early developments in the field. Some quasi-Bayesian procedures have been proposed, but often these approaches rely on heuristic, sometimes flawed, arguments. In this talk I will discuss some formulations of classical causal inference problems from the perspective of standard Bayesian representations, and propose some inferential solutions. This is joint work with Olli Saarela, Dalla Lana School of Public Health, University of Toronto, Erica Moodie, Department of Epidemiology, Biostatistics and Occupational Health, McGill University, and Marina Klein, Division of Infectious Diseases, Faculty of Medicine, McGill University.