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

Past Seminar Series

  • Free energy fluctuations of spherical spin glasses near the critical temperature threshold

    Elizabeth Collins-Woodfin · Apr 12, 2024

    Date: 2024-04-12

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

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/86957985232

    Meeting ID: 869 5798 5232

    Passcode: None

    Abstract:

    One of the fascinating phenomena of spin glasses is the dramatic change in behavior that occurs between the high and low temperature regimes. In addition to its physical meaning, this phase transition corresponds to a detection threshold with respect to the signal-to-noise ratio in a spiked matrix model. The free energy of the spherical Sherrington-Kirkpatrick (SSK) model has Gaussian fluctuations at high temperature, but Tracy-Widom fluctuations at low temperature. A similar phenomenon holds for the bipartite SSK model, and we show that, when the temperature is within a small window around the critical temperature, the free energy fluctuations converge to an independent sum of Gaussian and Tracy-Widom random variables (joint work with Han Le). Our work follows two recent papers that proved similar results for the SSK model (by Landon and by Johnstone, Klochkov, Onatski, Pavlyshyn). From a statistical perspective, the free energy of SSK and bipartite SSK correspond to log-likelihood ratios for spiked Wigner and spiked Wishart matrices respectively. Analyzing bipartite SSK at critical temperature requires a variety of tools including classical random matrix results, contour integral techniques, and a CLT for the log-characteristic polynomial of Wishart random matrices evaluated near the spectral edge.

  • Minimum Covariance Determinant: Spectral Embedding and Subset Size Determination

    Qiang Heng · Mar 22, 2024

    Date: 2024-03-22

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

    Location: Online, retransmitted in Burnside 1104

    https://mcgill.zoom.us/j/81895414756

    Meeting ID: 818 9541 4756

    Passcode: None

    Abstract:

    This paper introduces several enhancements to the minimum covariance determinant method of outlier detection and robust estimation of means and covariances. We leverage the principal component transform to achieve dimension reduction and ultimately better analyses. Our best subset selection algorithm strategically combines statistical depth and concentration steps. To ascertain the appropriate subset size and number of principal components, we introduce a bootstrap procedure that estimates the instability of the best subset algorithm. The parameter combination exhibiting minimal instability proves ideal for the purposes of outlier detection and robust estimation. Rigorous benchmarking against prominent MCD variants showcases our approach’s superior statistical performance and computational speed in high dimensions. Application to a fruit spectra data set and a cancer genomics data set illustrates our claims.

  • Recent advances in causal inference under irregular and informative observation times for the outcome

    Janie Coulombe · Mar 1, 2024

    Date: 2024-03-01

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

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/89811237909

    Meeting ID: 898 1123 7909

    Passcode: None

    Abstract:

    Electronic health records (EHR) data contain rich information about patients’ health condition, comorbidities, clinical outcomes, and drug prescriptions. They are often used to draw causal inferences and compare different treatments’ effectiveness. However, these data are not experimental. They present with special features that should be addressed or that may affect the inference. One of these features is the irregular observation of the longitudinal processes used in the inference. In longitudinal studies in which we seek the causal effect of a treatment on a repeated outcome, for instance, covariate-dependent observation of the outcome has been shown to bias standard causal estimators. In this presentation, I will review recent work and present some of the most interesting findings in this area of research. Themes will include identifiability, efficiency, and alternatives to weighting methods to address irregular observation times.

  • Matrix completion in genetic methylation studies: LMCC, a Linear Model of Coregionalization with informative Covariates

    Karim Oualkacha · Feb 16, 2024

    Date: 2024-02-16

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

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/82678428848

    Meeting ID: 826 7842 8848

    Passcode: None

    Abstract:

    DNA methylation is an important epigenetic mark that modulates gene expression through the inhibition of transcriptional proteins binding to DNA. As in many other omics experiments, missing values is an issue and appropriate imputation techniques are important to avoid an unnecessary sample size reduction as well as to optimally leverage the information collected. We consider the case where a relatively small number of samples are processed via an expensive high-density Whole Genome Bisulfite Sequencing (WGBS) strategy and a larger number of samples are processed using more affordable low-density array-based technologies. In such cases, one can impute/complete the data matrix of the low coverage (array-based) methylation data using the high-density information provided by the WGBS samples. In this work, we propose an efficient Linear Model of Coregionalization with informative Covariates (LMCC) to predict missing values based on observed values and informative covariates. Our model assumes that at each genomics position, the methylation vector of all samples is linked to the set of fixed factors (covariates) and a set of latent factors. Furthermore, we exploit the functional nature of the data and the spatial correlation across positions/sites by assuming Gaussian processes on the fixed and latent coefficient vectors, respectively. Our simulations show that the use of covariates can significantly improve the accuracy of imputed values, especially in cases where missing data contain some relevant information about the explanatory variable. We also show that the proposed model is efficient when the number of columns is much greater than the number of rows in the data matrix-which is usually the case in methylation data analysis. Finally, we apply and compare the proposed method with alternative approaches to complete a matrix of DNA methylation containing 15 rows (methylation samples) and 1 million columns (sites). Joint work with Melina Ribaud and Aurelie Labbe (HEC, Montreal).

  • Mesoscale two-sample testing for networks

    Peter William MacDonald · Feb 9, 2024

    Date: 2024-02-09

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

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/87465663442

    Meeting ID: 874 6566 3442

    Passcode: None

    Abstract:

    Networks arise naturally in many scientific fields as a representation of pairwise connections. Statistical network analysis has most often considered a single large network, but it is common in a number of applications, for example, neuroimaging, to observe multiple networks on a shared node set. When these networks are grouped by case-control status or another categorical covariate, the classical statistical question of two-sample comparison arises. In this work, we address the problem of testing for statistically significant differences in a prespecified subset of the connections. This general framework allows an analyst to focus on a single node, a specific region of interest, or compare whole networks. In this “mesoscale” setting, we develop statistically sound projection-based tests for two-sample comparison in both weighted and binary edge networks. Our approach can leverage all available network information, and learn informative projections which improve testing power when low-dimensional network structure is present.

  • Fast calibration of FARIMA models with dependent errors

    Youssef Esstafa · Feb 2, 2024

    Date: 2024-02-02

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

    Location: Online, retransmitted in Burnside 1104

    https://mcgill.zoom.us/j/89669635642

    Meeting ID: 896 6963 5642

    Passcode: None

    Abstract:

    In this work, we investigate the asymptotic properties of Le Cam’s one-step estimator for weak Fractionally AutoRegressive Integrated Moving-Average (FARIMA) models. For these models, noises are uncorrelated but neither necessarily independent nor martingale differences errors. We show under some regularity assumptions that the one-step estimator is strongly consistent and asymptotically normal with the same asymptotic variance as the least squares estimator. We show through simulations that the proposed estimator reduces computational time compared with the least squares estimator.

  • Imaging and Clinical Biomarker Estimation in Alzheimer’s Disease

    Ani Eloyan · Jan 19, 2024

    Date: 2024-01-19

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

    Location: Online, retransmitted in Burnside 1104

    https://mcgill.zoom.us/j/85422946487

    Meeting ID: 854 2294 6487

    Passcode: None

    Abstract:

    Estimation of biomarkers related to disease classification and modeling of its progression is essential for treatment development for Alzheimer’s Disease (AD). The task is more daunting for characterizing relatively rare AD subtypes such as the early-onset AD. In this talk, I will describe the Longitudinal Alzheimer’s Disease Study (LEADS) intending to collect and publicly distribute clinical, imaging, genetic, and other types of data from people with EOAD, as well as cognitively normal (CN) controls and people with early-onset non-amyloid positive (EOnonAD) dementias. I will discuss manifold estimation methods for estimation of surfaces of shapes in the brain using data clouds, longitudinal manifold learning methods for modeling trajectories of shape changes in the brain over time. Finally, I will discuss our work in leveraging magnetic resonance imaging and positron emission tomography data to characterize distributions of white matter hyperintensities in people with EOAD and to obtain imaging-based biomarkers of disease trajectories of AD subtypes.

  • New Advances in High-Dimensional DNA Methylation Analysis in Cancer Epigenetic Using Trans-dimensional Hidden Markov Models

    Farhad Shokoohi · Jan 12, 2024

    Date: 2024-01-12

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

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/83008174313

    Meeting ID: 830 0817 4313

    Passcode: None

    Abstract:

    Epigenetic alterations are key drivers in the development and progression of cancer. Identifying differentially methylated cytosines (DMCs) in cancer samples is a crucial step toward understanding these changes. In this talk, we propose a trans-dimensional Markov chain Monte Carlo (TMCMC) approach that uses hidden Markov models (HMMs) with binomial emission, and bisulfite sequencing (BS-Seq) data, called DMCTHM, to identify DMCs in cancer epigenetic studies. We introduce the Expander-Collider penalty to tackle under and over-estimation in TMCMC-HMMs. We address all known challenges inherent in BS-Seq data by introducing novel approaches for capturing functional patterns and autocorrelation structure of the data, as well as for handling missing values, multiple covariates, multiple comparisons, and family-wise errors. We demonstrate the effectiveness of DMCTHM through comprehensive simulation studies. The results show that our proposed method outperforms other competing methods in identifying DMCs. Notably, with DMCTHM, we uncovered new DMCs and genes in Colorectal cancer that were significantly enriched in the Tp53 pathway.

  • Robust and Tuning-Free Sparse Linear Regression via Square-Root Slope

    Mohamed Ndaoud · Nov 17, 2023

    Date: 2023-11-17

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

    Location: Online, retransmitted in Burnside 1104

    https://mcgill.zoom.us/j/81865630475

    Meeting ID: 818 6563 0475

    Passcode: None

    Abstract:

    We consider the high-dimensional linear regression model and assume that a fraction of the responses are contaminated by an adversary with complete knowledge of the data and the underlying distribution. We are interested in the situation when the dense additive noise can be heavy-tailed but the predictors have sub-Gaussian distribution. We establish minimax lower bounds that depend on the fraction of the contaminated data and the tails of the additive noise. Moreover, we design a modification of the square root Slope estimator with several desirable features: (a) it is provably robust to adversarial contamination, with the performance guarantees that take the form of sub-Gaussian deviation inequalities and match the lower error bounds up to log-factors; (b) it is fully adaptive with respect to the unknown sparsity level and the variance of the noise, and (c) it is computationally tractable as a solution of a convex optimization problem. To analyze the performance of the proposed estimator, we prove several properties of matrices with sub-Gaussian rows that could be of independent interest. This is joint work with Stanislav Minsker and Lang Wang.

  • Copula-based estimation of health inequality measures

    Taoufik Bouezmarni · Nov 10, 2023

    Date: 2023-11-10

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

    Location: In person, Burnside 1104

    https://mcgill.zoom.us/j/89337793218

    Meeting ID: 893 3779 3218

    Passcode: None

    Abstract:

    This paper aims to use copulas to derive estimators of the health concentration curve and Gini coefficient for health distribution. We highlight the importance of expressing health inequality measures in terms of a copula, which we in turn use to build copula-based semi and nonparametric estimators of the above measures. Thereafter, we study the asymptotic properties of these estimators. In particular, we establish their consistency and asymptotic normality. We provide expressions for their variances, which can be used to construct confidence intervals and build tests for the health concentration curve and Gini health coefficient. A Monte-Carlo simulation exercise shows that the semiparametric estimator outperforms the smoothed nonparametric estimator, and the latter does better than the empirical estimator in terms of Mean Squared Error. We also run an extensive empirical study where we apply our estimators to show that the inequalities across U.S. states’s socioeconomic variables like income/poverty and race/ethnicity explain the observed inequalities in COVID-19 infections and deaths in the U.S.