September 9, 2016

McGill Statistics Seminar

Fei Gu

Twoset canonical variate model in multiple populations with invariant loadings 
15:3016:30

BURN 1205 
Abstract: 
Goria and Flury (Definition 2.1, 1996) proposed the twoset canonical variate model (referred to as the CV2 model hereafter) and its extension in multiple populations with invariant weight coefficients (Definition 2.2). The equality constraints imposed on the weight coefficients are in line with the approach to interpreting the canonical variates (i.e., the linear combinations of original variables) advocated by Harris (1975, 1989), Rencher (1988, 1992), and Rencher and Christensen (2003). However, the literature in psychology and education shows that the standard approach adopted by most researchers, including Anderson (2003), is to use the canonical loadings (i.e., the correlations between the canonical variates and the original variables in the same set) to interpret the canonical variates. In case of multicollinearity (giving rise to the socalled suppression effects) among the original variables, it is not uncommon to obtain different interpretations from the two approaches. Therefore, following the standard approach in practice, an alternative (probably more realistic) extension of Goria and Flury’s CV2 model in multiple populations is to impose the equality constraints on the canonical loadings. The utility of this multiplepopulation extension are illustrated with two numeric examples.

Speaker: 
Fei Gu is an Assistant Professor at the Department of Psychology, McGill University. 

September 16, 2016

CRM Colloque de statistique

Prakasa Rao

Statistical inference for fractional diffusion processes 
16:0017:00

LB921.04, Library Building, Concordia Univ. 
Abstract: 
There are some time series which exhibit longrange dependence as noticed by Hurst in his investigations of river water levels along Nile river. Longrange dependence is connected with the concept of selfsimilarity in that increments of a selfsimilar process with stationary increments exhibit longrange dependence under some conditions. Fractional Brownian motion is an example of such a process. We discuss statistical inference for stochastic processes modeled by stochastic differential equations driven by a fractional Brownian motion. These processes are termed as fractional diffusion processes. Since fractional Brownian motion is not a semimartingale, it is not possible to extend the notion of a stochastic integral with respect to a fractional Brownian motion following the ideas of Ito integration. There are other methods of extending integration with respect to a fractional Brownian motion. Suppose a complete path of a fractional diffusion process is observed over a finite time interval. We will present some results on inference problems for such processes.

Speaker: 
Dr. B.L.S. Prakasa Rao is Ramanujan Chair Professor at CR Rao Advanced Institute, Hyderabad, India 

September 23, 2016 
McGill Statistics Seminar

JeanFrançois Coeurjolly

Stein estimation of the intensity parameter of a stationary spatial Poisson point process

15:3016:30

BURN 1205 
Abstract: 
We revisit the problem of estimating the intensity parameter of a homogeneous Poisson point process observed in a bounded window of $R^d$ making use of a (now) old idea going back to James and Stein. For this, we prove an integration by parts formula for functionals defined on the Poisson space. This formula extends the one obtained by Privault and Réveillac (Statistical inference for Stochastic Processes, 2009) in the onedimensional case and is wellsuited to a notion of derivative of Poisson functionals which satisfy the chain rule. The new estimators can be viewed as biased versions of the MLE with a tailoredmade bias designed to reduce the variance of the MLE. We study a large class of examples and show that with a controlled probability the corresponding estimator outperforms the MLE. We illustrate in a simulation study that for very reasonable practical cases (like an intensity of 10 or 20 of a Poisson point process observed in the ddimensional euclidean ball of with d = 1, ..., 5), we can obtain a relative (mean squared error) gain above 20% for the Stein estimator with respect to the maximum likelihood. This is a joint work with M. Clausel and J. Lelong (Univ. Grenoble Alpes, France).

Speaker: 
JeanFrançois Coeurjolly is a Professor in the Department of Mathematics at Université du Québec à Montréal (UQÀM). 

September 30, 2016

McGill Statistics Seminar

Hui Zou

CoCoLasso for highdimensional errorinvariables regression 
15:3016:30

BURN 1205 
Abstract: 
Much theoretical and applied work has been devoted to highdimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright (2012) proposed a nonconvex modification of the Lasso for doing highdimensional regression with noisy and missing data. It is generally agreed that the virtues of convexity contribute fundamentally the success and popularity of the Lasso. In light of this, we propose a new method named CoCoLasso that is convex and can handle a general class of corrupted datasets including the cases of additive measurement error and random missing data. We establish the estimation error bounds of CoCoLasso and its asymptotic signconsistent selection property. We further elucidate how the standard cross validation techniques can be misleading in presence of measurement error and develop a novel corrected crossvalidation technique by using the basic idea in CoCoLasso. The corrected crossvalidation has its own importance. We demonstrate the superior performance of our method over the nonconvex approach by simulation studies.

Speaker: 
Hui Zou is a Professor in the School of Statistics at the University of Minnesota. 

October 7, 2016

McGill Statistics Seminar

Luc Devroye

Cellular tree classifiers 
15:3016:30

BURN 1205 
Abstract: 
Suppose that binary classification is done by a tree method in which the leaves of a tree correspond to a partition of dspace. Within a partition, a majority vote is used. Suppose furthermore that this tree must be constructed recursively by implementing just two functions, so that the construction can be carried out in parallel by using "cells": first of all, given input data, a cell must decide whether it will become a leaf or internal node in the tree. Secondly, if it decides on an internal node, it must decide how to partition the space linearly. Data are then split into two parts and sent downstream to two new independent cells. We discuss the design and properties of such classifiers.

Speaker: 
Luc P. Devroye is a James McGill Professor in the School of Computer Science of McGill University. Since joining the McGill faculty in 1977 he has won numerous awards, including an E.W.R. Steacie Memorial Fellowship (1987), a Humboldt Research Award (2004), the Killam Prize (2005) and the Statistical Society of Canada gold medal (2008). He received an honorary doctorate from the Université catholique de Louvain in 2002, and he received an honorary doctorate from Universiteit Antwerpen on March 29, 2012. 

October 14, 2016

McGill Statistics Seminar

Geneviève Lefebvre

A Bayesian finite mixture of bivariate regressions model for causal mediation analyses 
15:3016:30

BURN 1205 
Abstract: 
Building on the work of Schwartz, Gelfand and Miranda (Statistics in Medicine (2010); 29(16), 171023), we propose a Bayesian finite mixture of bivariate regressions model for causal mediation analyses. Using an identifiability condition within each component of the mixture, we express the natural direct and indirect effects of the exposure on the outcome as functions of the componentspecific regression coefficients. On the basis of simulated data, we examine the behaviour of the model for estimating these effects in situations where the associations between exposure, mediator and outcome are confounded, or not. Additionally, we demonstrate that this mixture model can be used to account for heterogeneity arising through unmeasured binary mediatoroutcome confounders. Finally, we apply our mediation mixture model to estimate the natural direct and indirect effects of exposure to inhaled corticosteroids during pregnancy on birthweight using a cohort of asthmatic women from the province of Québec.

Speaker: 
Geneviève Lefebvre is an Associate Professor in the Department of Mathematics at the Université du Québec à Montréal (UQAM) 

October 21, 2016 
McGill Statistics Seminar

ChienLin Su

Statistical analysis of twolevel hierarchical clustered data

15:3016:30

BURN 1205 
Abstract: 
Multilevel hierarchical clustered data are commonly seen in financial and biostatistics applications. In this talk, we introduce several modeling strategies for describing the dependent relationships for members within a cluster or between different clusters (in the same or different levels). In particular we will apply the hierarchical Kendall copula, first proposed by Brechmann (2014), to model twolevel hierarchical clustered survival data. This approach provides a clever way of dimension reduction in modeling complicated multivariate data. Based on the model assumptions, we propose statistical inference methods, including parameter estimation and a goodnessoffit test, suitable for handling censored data. Simulation and data analysis results are also presented.

Speaker: 
ChienLin Su is a postdoc fellow under the supervision of Professor Russell Steele (McGill) and Lajmi LakhalChaieb (Laval). He received his Master's degree in mathematics in 2009 and PhD degree in statistics from National Chiao Tung University (NCTU), Taiwan in 2015. His research interests include multivariate survival analysis and copula research in biomedical and financial applications. He received a grant from National Science Council (NSC) of Taiwan and conducted research as a research trainee with the supervision of Professor Johanna G. Nešlehová from July 2013 to February 2014. 

October 28, 2016

CRM Colloque de statistique

Jerry Lawless

Efficient tests of covariate effects in twophase failure time studies 
15:3016:30

BURN 1205 
Abstract: 
Twophase studies are frequently used when observations on certain variables are expensive or difficult to obtain. One such situation is when a cohort exists for which certain variables have been measured (phase 1 data); then, a subsample of individuals is selected, and additional data are collected on them (phase 2). Efficiency for tests and estimators can be increased by basing the selection of phase 2 individuals on data collected at phase 1. For example, in large cohorts, expensive genomic measurements are often collected at phase 2, with oversampling of persons with “extreme” phenotypic responses. A second example is casecohort or nested casecontrol studies involving times to rare events, where phase 2 oversamples persons who have experienced the event by a certain time. In this talk I will describe twophase studies on failure times, present efficient methods for testing covariate effects. Some extensions to more complex outcomes and areas needing further development will be discussed.

Speaker: 
Jerry Lawless is a Distinguished Professor Emeritus in the Department of Statistics and Actuarial Science at the University of Waterloo. He has been a consultant to industry and government, is a past editor of Technometrics and a past president of the Statistical Society of Canada. He is a Fellow of the American Statistical Association (1983) and of the Institute of Mathematical Statistics (1990), and a recipient of the Gold Medal of the Statistical Society of Canada (1999). He was elected a Fellow of the Royal Society of Canada in 2000. 

November 2, 2016

McGill Statistics Seminar

Tim Hesterberg

First talk: Bootstrap in practice
Second talk: Statistics and Big Data at Google

1. 15:0016:00
2. 17:3518:25

1st: BURN 306
2nd: ADAMS AUD 
Abstract: 
First talk: This talk focuses on three practical aspects of resampling: communication, accuracy, and software. I'll introduce the bootstrap and permutation tests, and discussed how they may be used to help clients understand statistical results. I'll talk about accuracy  there are dramatic differences in how accurate different bootstrap methods are. Surprisingly, the most common bootstrap methods are less accurate than classical methods for small samples, and more accurate for larger samples. There are simple variations that dramatically improve the accuracy. Finally, I'll compare two R packages, the the easytouse "resample" package, and the morepowerful "boot" package.
Second talk: Google lives on data. Search, Ads, YouTube, Maps, ...  they all live on data. I'll tell stories about how we use data, how we're always experimenting to make improvements (yes, this includes your searches), and how we adapt statistical ideas to do things that have never been done before.

Speaker: 
Tim Hesterberg is a Senior Statistician at Google. He received his PhD in Statistics from Stanford University, under Brad Efron. He is on the executive boards of the National Institute of Statistical Sciences and the Interface Foundation of North America (Interface between Computing Science and Statistics). 

November 4, 2016

McGill Statistics Seminar

Sean Lawlor and Alexandre Piché

Lawlor: Timevarying mixtures of Markov chains: An application to traffic modeling
Piché: Bayesian nonparametric modeling of heterogeneous groups of censored data

15:3016:30

BURN 1205 
Abstract: 
Piché: Analysis of survival data arising from different groups, whereby the data in each group is scarce, but abundant overall, is a common issue in applied statistics. Bayesian nonparametrics are tools of choice to handle such datasets given their ability to share information across groups. In this presentation, we will compare three popular Bayesian nonparametric methods on the modeling of survival functions coming from related heterogeneous groups. Specifically, we will first compare the modeling accuracy of the Dirichlet process, the hierarchical Dirichlet process, and the nested Dirichlet process on simulated datasets of different sizes, where groups differ in shape or in expectation, and finally we will compare the models on real world injury datasets.
Lawlor: Timevarying mixture models are useful for representing complex, dynamic distributions. Components in the mixture model can appear and disappear, and persisting components can evolve. This allows great flexibility in streaming data applications where the model can be adjusted as new data arrives. Fitting a mixture model, especially when the model order varies with time, with computational guarantees which can meet realtime requirements is difficult with existing algorithms. Multiple issues exist with existing approximate inference methods ranging from estimation of the model order to random restarts due to the ability to converge to different local minima. MonteCarlo methods can be used to estimate the parameters of the generating distribution and estimate the model order, but when the distribution of each mixand has a highdimensional parameter space, they suffer from the curse of dimensionality and can take far too long to converge. This paper proposes a generative model for timevarying mixture models, tailored for mixtures of discretetime Markov chains. A novel, deterministic inference procedure is introduced and is shown to be suitable for applications requiring realtime estimation. The method is guaranteed to converge to a local maximum of the posterior likelihood at each time step with a computational complexity which is low enough for realtime applications. As a motivating application, we model and predict traffic patterns in a transportation network. Experiments illustrate the performance of the scheme and offer insights regarding tuning of the parameters of the algorithm. The experiments also investigate the predictive power of the fitted model compared to less complex models and demonstrate the superiority of the mixture model approach for prediction of traffic routes in real data.

Speaker: 
Sean Lawlor is a Doctoral Candidate in Electrical Engineering from the Department of Electrical and Computer Engineering, McGill University
Alexandre Piché is a MSc student in our Department. His supervisor is Russell Steele.


November 11, 2016

McGill Statistics Seminar

Teng Zhang

Tyler's Mestimator: Subspace recovery and highdimensional regime 
15:3016:30

BURN 1205 
Abstract: 
Given a data set, Tyler's Mestimator is a widely used covariance matrix estimator with robustness to outliers or heavytailed distribution. We will discuss two recent results of this estimator. First, we show that when a certain percentage of the data points are sampled from a lowdimensional subspace, Tyler's Mestimator can be used to recover the subspace exactly. Second, in the highdimensional regime that the number of samples n and the dimension p both go to infinity, p/n converges to a constant y between 0 and 1, and when the data samples are identically and independently generated from the Gaussian distribution N(0,I), we showed that the difference between the sample covariance matrix and a scaled version of Tyler's Mestimator tends to zero in spectral norm, and the empirical spectral densities of both estimators converge to the MarcenkoPastur distribution. We also prove that when the data samples are generated from an elliptical distribution, the limiting distribution of Tyler's Mestimator converges to a MarcenkoPasturType distribution. The second part is joint work with Xiuyuan Cheng and Amit Singer.

Speaker: 
Teng Zhang is an Assistant Professor in the Department of Mathematics at the University of Central Florida. 

November 18, 2016

McGill Statistics Seminar

Yoshua Bengio

Progress in theoretical understanding of deep learning 
15:3016:30

BURN 1205 
Abstract: 
Deep learning has arisen around 2006 as a renewal of neural networks research allowing such models to have more layers. Theoretical investigations have shown that functions obtained as deep compositions of simpler functions (which includes both deep and recurrent nets) can express highly varying functions (with many ups and downs and different input regions that can be distinguished) much more efficiently (with fewer parameters) than otherwise, under a prior which seems to work well for artificial intelligence tasks. Empirical work in a variety of applications has demonstrated that, when well trained, such deep architectures can be highly successful, remarkably breaking through previous stateoftheart in many areas, including speech recognition, object recognition, language models, machine translation and transfer learning. Although neural networks have long been considered lacking in theory and much remains to be done, theoretical advances have been made and will be discussed, to support distributed representations, depth of representation, the nonconvexity of the training objective, and the probabilistic interpretation of learning algorithms (especially of the autoencoder type, which were lacking one). The talk will focus on the intuitions behind these theoretical results.

Speaker: 
Yoshua Bengio is a Professor of the Department of Computer Science and Operations Research at the University of Montreal, head of the Montreal Institute for Learning Algorithms (MILA), CIFAR Program codirector of the CIFAR Neural Computation and Adaptive Perception program, Canada Research Chair in Statistical Learning Algorithms. 

November 25, 2016 
McGill Statistics Seminar

Alexandra Schmidt

Spatiotemporal models for skewed processes

15:3016:30

BURN 1205 
Abstract: 
In the analysis of most spatiotemporal processes in environmental studies, observations present skewed distributions. Usually, a single transformation of the data is used to approximate normality, and stationary Gaussian processes are assumed to model the transformed data. The choice of transformation is key for spatial interpolation and temporal prediction. We propose a spatiotemporal model for skewed data that does not require the use of data transformation. The process is decomposed as the sum of a purely temporal structure with two independent components that are considered to be partial realizations from independent spatial Gaussian processes, for each time t. The model has an asymmetry parameter that might vary with location and time, and if this is equal to zero, the usual Gaussian model results. The inference procedure is performed under the Bayesian paradigm, and uncertainty about parameters estimation is naturally accounted for. We fit our model to different synthetic data and to monthly average temperature observed between 2001 and 2011 at monitoring locations located in the south of Brazil. Different model comparison criteria, and analysis of the posterior distribution of some parameters, suggest that the proposed model outperforms standard ones used in the literature. This is joint work with Kelly Gonçalves (UFRJ, Brazil) and Patricia L. Velozo (UFF, Brazil)

Speaker: 
Alexandra M. Schmidt is an Associate Professor of Biostatistics in the Department of Epidemiology, Biostatistics, and Occupational Health at McGill University. 

December 1, 2016

CRM Colloque de statistique

Richard Samworth

Highdimensional changepoint estimation via sparse projection 
15:3016:30

BURN 708 
Abstract: 
Changepoints are a very common feature of Big Data that arrive in the form of a data stream. We study highdimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the coordinates. The challenge is to borrow strength across the coordinates in order to detect smaller changes than could be observed in any individual component series. We propose a twostage procedure called 'inspect' for estimation of the changepoints: first, we argue that a good projection direction can be obtained as the leading left singular vector of the matrix that solves a convex optimisation problem derived from the CUSUM transformation of the time series. We then apply an existing univariate changepoint detection algorithm to the projected series. Our theory provides strong guarantees on both the number of estimated changepoints and the rates of convergence of their locations, and our numerical studies validate its highly competitive empirical performance for a wide range of data generating mechanisms.

Speaker: 
Richard Samworth is a Professor of Statistics in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. He is a Fellow of the American Statistical Association (2015) and of the Institute of Mathematical Statistics (2014), and a recipient of the Philip Leverhulme Prize, Leverhulme Trust (2014) and the Guy Medal in Bronze, Royal Statistical Society (2012). 

December 2, 2016

McGill Statistics Seminar

Andrea Giussani

Modeling dependence in bivariate multistate processes: A frailty approach 
15:3016:30

BURN 1205 
Abstract: 
The aim of this talk is to present a statistical framework for the analysis of dependent bivariate multistate processes, allowing one to study the dependence both across subjects in a pair and among individualspecific events. As for the latter, copula based models are employed, whereas dependence between multistate models can be accomplished by means of frailties. The well known MarshallOlkin Bivariate Exponential Distribution (MOBVE) is considered for the joint distribution of frailties. The reason is twofold: on the one hand, it allows one to model shocks that affect the two individualspecific frailties; on the other hand, the MOBVE is the only bivariate exponential distribution with exponential marginals, which allows for the modeling of each multistate process as a shared frailty model. We first discuss a frailty bivariate survival model with some new results, and then move to the construction of the frailty bivariate multistate model, with the corresponding observed data likelihood maximization estimating procedure in presence of right censoring. The last part of the talk will be dedicated to some open problems related to the modeling of multiple multistate processes in presence of MarshallOlkin type copulas.

Speaker: 
Andrea Giussani is a PhD candidate in Statistics at Bocconi University, Milan (Italy). His current scientific research is focused on eventhistory and survival data analysis. 
