/tags/2024-fall/index.xml 2024 Fall - McGill Statistics Seminars

2024 Fall

  • Goodness-of-Fit Testing for the Wishart Distributions

    Donald Richards · Dec 13, 2024

    Date: 2024-12-13

    Time: 15:30-16:30 (Montreal time)

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/81501161882

    Meeting ID: 815 0116 1882

    Passcode: None

    Abstract:

    The problem of testing that a random sample is drawn from a specific probability distribution is an old one, the most famous example perhaps being the problem of testing that a sequence of playing cards was drawn from a fairly shuffled deck. In recent years, random data consisting of positive definite (symmetric) matrices have appeared in areas of applied research such as factor analysis, diffusion tensor imaging, wireless communication systems, synthetic aperture radar, and models of financial volatility. Given a random sample of positive definite matrices, we develop a goodness-of-fit test for the Wishart distributions. We derive the asymptotic distribution of the test statistic in terms of a certain Gaussian random field, and we obtain an explicit formula for the corresponding covariance operator. The eigenfunctions of the covariance operator are determined explicitly, and the eigenvalues are shown to satisfy certain interlacing properties. As an application, we carry out a test that a financial data set has a Wishart distribution and, finally, we describe some recent research and open problems on related goodness-of-fit tests.

  • Conditional nonparametric variable screening via neural network factor regression

    Yue Zhao · Dec 6, 2024

    Date: 2024-12-06

    Time: 15:30-16:30 (Montreal time)

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/83785721810

    Meeting ID: 837 8572 1810

    Passcode: None

    Abstract:

    High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to their representation power. We ask the question whether individual covariates have additional contributions given the latent factors. Our test statistics are based on the estimated partial derivative of the regression function of the candidate variable for screening and an observable proxy for the latent factors. Hence, our test reveals how much predictors contribute additionally to the non-parametric regression after accounting for the latent factors. Our derivative estimator is the convolution of a deep neural network regression estimator and a smoothing kernel. We demonstrate that when the neural network size diverges with the sample size, unlike estimating the regression function itself, it is necessary to smooth the partial derivative of the neural network estimator to recover the desired convergence rate for the derivative. Moreover, our screening test achieves asymptotic normality under the null after finely centering our test statistics that makes the biases negligible, as well as consistency for local alternatives under mild conditions. We demonstrate the performance of our test in a simulation study and a real world application.

  • Asymptotic behavior of data driven empirical measures for testing multivariate regular variation

    Benjamin Bobbia · Nov 22, 2024

    Date: 2024-11-22

    Time: 15:30-16:30 (Montreal time)

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/82125361063

    Meeting ID: 821 2536 1063

    Passcode: None

    Abstract:

    Nowadays, empirical processes are well known objects. A reason that push forward theirs studies is that, in many models, we can write the estimators as images of empirical measures. In this work, the interest is touched upon the case of local empirical measures built over a sub-sample of data conditioned to be in a certain area, itself depending on the data. In the present work we present a general framework which allows to derive asymptotic results for these empirical measures. This approach is specified for the framework of extreme values theory. As an application, an asymptotic result allowing to derive a test procedure for Multivariate Regular Variation is detailed.

  • Practical existence theorems for deep learning approximation in high dimensions

    Simone Brugiapaglia · Nov 15, 2024

    Date: 2024-11-15

    Time: 15:30-16:30 (Montreal time)

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/89043936588

    Meeting ID: 890 4393 6588

    Passcode: None

    Abstract:

    Deep learning is having a profound impact on industry and scientific research. Yet, while this paradigm continues to show impressive performance in a wide variety of applications, its mathematical foundations are far from being well understood. Motivated by deep learning methods for scientific computing, I will present new practical existence theorems that aim at bridging the gap between theory and practice in this area. Combining universal approximation results for deep neural networks with sparse high-dimensional polynomial approximation theory, these theorems identify sufficient conditions on the network architecture, the training strategy, and the size of the training set able to guarantee a target accuracy. I will illustrate practical existence theorems in the contexts of high-dimensional function approximation via feedforward networks, reduced order modeling based on convolutional autoencoders, and physics-informed neural networks for high-dimensional PDEs.

  • A latent-vine factor-copula time series model for extreme flood insurance losses

    Christian Genest · Nov 8, 2024

    Date: 2024-11-08

    Time: 15:30-16:30 (Montreal time)

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/89121567327

    Meeting ID: 891 2156 7327

    Passcode: None

    Abstract:

    Vines and factor copula models are handy tools for statistical inference in high dimension. However, their use for assessing and predicting the co-occurrence of rare events is subject to caution when multivariate extreme data are sparse. Motivated by the need to assess the risk of concurrent large insurance claims in the American National Flood Insurance Program (NFIP), I will describe a novel class of copula models that can account for spatio-temporal dependence within clustered sets of time series. This new class, which combines the advantages of vines and factor copula models, provides great flexibility in capturing tail dependence while maintaining interpretability through a parsimonious latent structure. Using NFIP data, I will show the value of this approach in evaluating the risks associated with extreme weather events.

  • On Mixture of Experts in Large-Scale Statistical Machine Learning Applications

    Nhat Ho · Nov 1, 2024

    Date: 2024-11-01

    Time: 15:30-16:30 (Montreal time)

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/81284191962

    Meeting ID: 812 8419 1962

    Passcode: None

    Abstract:

    Mixtures of experts (MoEs), a class of statistical machine learning models that combine multiple models, known as experts, to form more complex and accurate models, have been combined into deep learning architectures to improve the ability of these architectures and AI models to capture the heterogeneity of the data and to scale up these architectures without increasing the computational cost. In mixtures of experts, each expert specializes in a different aspect of the data, which is then combined with a gating function to produce the final output. Therefore, parameter and expert estimates play a crucial role by enabling statisticians and data scientists to articulate and make sense of the diverse patterns present in the data. However, the statistical behaviors of parameters and experts in a mixture of experts have remained unsolved, which is due to the complex interaction between gating function and expert parameters.

  • New Statistical Methods and Quality Control for Industry 4.0

    Antonio Lepore · Oct 25, 2024

    Date: 2024-10-25

    Time: 15:30-16:30 (Montreal time)

    Location: Online, retransmitted in Burnside 1104

    https://mcgill.zoom.us/j/81908885431

    Meeting ID: 819 0888 5431

    Passcode: None

    Abstract:

    Statistical and machine learning techniques have emerged as powerful tools in Industry 4.0 to benefit from the increasing availability of sensors and data and enable informed decision-making and process optimization. This seminar will provide an overview of several industrial applications in high-dimensional settings developed by the Statistics for Engineering Research (SFERe) group (www.sfere.unina.it), affiliated with the Department of Industrial Engineering at the University of Naples FEDERICO II. In these applications, the definition and use of novel statistical methods have been a competitive advantage for naval, automotive, and rail companies. The open-source R software packages implementing these methods will also be mentioned to highlight their accessibility and potential applicability in different industrial contexts.

  • A functional data approach for statistical shapes analysis

    Issam Moindjié · Oct 11, 2024

    Date: 2024-10-11

    Time: 15:30-16:30 (Montreal time)

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/87824357176

    Meeting ID: 878 2435 7176

    Passcode: None

    Abstract:

    The shape $\tilde{\mathbf{X}}$ of a random planar curve, $\mathbf{X}$, is what remains when the deformation variables (scaling, rotation, translation, and reparametrization) are removed. Previous studies in statistical shape analysis have focused on analyzing $\tilde{\bf X}$ through discrete observations of ${\bf X}$. While this approach has some computational advantages, it overlooks the continuous nature of variables: $\tilde{\bf X}$, ${\bf X}$, and it ignores the potential dependence of deformation variables on each other and $\tilde{ \bf X}$, which results in a loss of information in the data structure. I will introduce a new framework for studying $\bf X$ based on functional data analysis in this presentation. Basis expansion techniques are employed to find analytic solutions for deformation variables such as rotation and parametrization deformations. Then, the generative model of $\bf X$ is investigated using a joint-principal component analysis approach. Numerical experiments on synthetic and real datasets demonstrate how this new approach performs better at analyzing random planar curves than traditional functional data methods.

  • VCBART: Bayesian trees for varying coefficients

    Ray Bai · Sep 27, 2024

    Date: 2024-09-27

    Time: 15:30-16:30 (Montreal time)

    Location: Online, retransmitted in Burnside 1104

    https://mcgill.zoom.us/j/88350756970

    Meeting ID: 883 5075 6970

    Passcode: None

    Abstract:

    The linear varying coefficient models posits a linear relationship between an outcome and covariates in which the covariate effects are modeled as functions of additional effect modifiers. Despite a long history of study and use in statistics and econometrics, state-of-the-art varying coefficient modeling methods cannot accommodate multivariate effect modifiers without imposing restrictive functional form assumptions or involving computationally intensive hyperparameter tuning. In response, we introduce VCBART which flexibly estimates the covariate effect in a varying coefficient model using Bayesian Additive Regression Trees. With simple default settings, VCBART outperforms existing varying coefficient methods in terms of covariate effect estimation, uncertainty quantification, and outcome prediction. Theoretically, we show that the VCBART posterior contracts at the near-minimax optimal rate. Finally, we illustrate the utility of VCBART through simulation studies and a real data application examining how the association between later-life cognition and measures of socioeconomic position vary with respect to age and sociodemographics.

  • Variance reduction by occluding a Markov chain

    Florian Maire · Sep 20, 2024

    Date: 2024-09-20

    Time: 15:30-16:30 (Montreal time)

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/88265323185

    Meeting ID: 882 6532 3185

    Passcode: None

    Abstract:

    Stochastic algorithms which simulate random variables/processes on a computer to estimate intractable quantities are ubiquitous in Statistics and elsewhere. One such method is Markov chain Monte Carlo which, under mild conditions, offer asymptotical (in time) guarantees. In this talk, we define infinitely many stopping times at which an ergodic Markov chain is occluded by a (conditionally) independent process. The resulting process, called the occluded process, is not Markov, but provided that the stopping times/independent process are cleverly defined, we show that it is ergodic. One particularly powerful way to define the stopping times/independent process leverages the recent advances in ML regarding approximations of probability distributions (divergence minimization, normalizing flows, etc.). We discuss the variance reduction effect of the occluded process through some illustrations and (weak) theoretical results in some limiting regime.