/categories/mcgill-statistics-seminar/index.xml McGill Statistics Seminar - McGill Statistics Seminars

McGill Statistics Seminar

  • Some development on dynamic computer experiments

    C. Devon Lin · Mar 23, 2018

    Date: 2018-03-23

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Computer experiments refer to the study of real systems using complex simulation models. They have been widely used as efficient, economical alternatives to physical experiments. Computer experiments with time series outputs are called dynamic computer experiments. In this talk, we consider two problems of such experiments: emulation of large-scale dynamic computer experiments and inverse problem. For the first problem, we proposed a computationally efficient modelling approach which sequentially finds a set of local design points based on a new criterion specifically designed for emulating dynamic computer simulators. Singular value decomposition based Gaussian process models are built with the sequentially chosen local data. To update the models efficiently, an empirical Bayesian approach is introduced. The second problem aims to extract an optimal input of dynamic computer simulator whose response matches a field observation as closely as possible. A sequential design approach is employed and a novel expected improvement criterion is proposed. A real application is discussed to support the efficiency of the proposed approaches.

  • Statistical Genomics for Understanding Complex Traits

    Sara Mostafavi · Mar 16, 2018

    Date: 2018-03-16

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Over the last decade, advances in measurement technologies has enabled researchers to generate multiple types of high-dimensional “omics” datasets for large cohorts. These data provide an opportunity to derive a mechanistic understanding of human complex traits. However, inferring meaningful biological relationships from these data is challenging due to high-dimensionality , noise, and abundance of confounding factors. In this talk, I’ll describe statistical approaches for robust analysis of genomic data from large population studies, with a focus on 1) understanding the nature of confounding and approaches for addressing them and 2) understanding the genomic correlates of aging and dementia.

  • Sparse Penalized Quantile Regression: Method, Theory, and Algorithm

    Yuwen Gu · Feb 23, 2018

    Date: 2018-02-23

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Sparse penalized quantile regression is a useful tool for variable selection, robust estimation, and heteroscedasticity detection in high-dimensional data analysis. We discuss the variable selection and estimation properties of the lasso and folded concave penalized quantile regression via non-asymptotic arguments. We also consider consistent parameter tuning therein. The computational issue of the sparse penalized quantile regression has not yet been fully resolved in the literature, due to non-smoothness of the quantile regression loss function. We introduce fast alternating direction method of multipliers (ADMM) algorithms for computing the sparse penalized quantile regression. Numerical examples demonstrate the competitive performance of our algorithm: it significantly outperforms several other fast solvers for high-dimensional penalized quantile regression.

  • Methodological considerations for the analysis of relative treatment effects in multi-drug-resistant tuberculosis from fused observational studies

    Mireille Schnitzer · Feb 9, 2018

    Date: 2018-02-09

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Multi-drug-resistant tuberculosis (MDR-TB) is defined as strains of tuberculosis that do not respond to at least the two most used anti-TB drugs. After diagnosis, the intensive treatment phase for MDR-TB involves taking several alternative antibiotics concurrently. The Collaborative Group for Meta-analysis of Individual Patient Data in MDR-TB has assembled a large, fused dataset of over 30 observational studies comparing the effectiveness of 15 antibiotics. The particular challenges that we have considered in the analysis of this dataset are the large number of potential drug regimens, the resistance of MDR-TB strains to specific antibiotics, and the identifiability of a generalized parameter of interest though most drugs were not observed in all studies. In this talk, I describe causal inference theory and methodology that we have appropriated or developed for the estimation of treatment importance and relative effectiveness of different antibiotic regimens with a particular emphasis on targeted learning approaches

  • A new approach to model financial data: The Factorial Hidden Markov Volatility Model

    Maciej Augustyniak · Feb 2, 2018

    Date: 2018-02-02

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    A new process, the factorial hidden Markov volatility (FHMV) model, is proposed to model financial returns or realized variances. This process is constructed based on a factorial hidden Markov model structure and corresponds to a parsimoniously parametrized hidden Markov model that includes thousands of volatility states. The transition probability matrix of the underlying Markov chain is structured so that the multiplicity of its second largest eigenvalue can be greater than one. This distinctive feature allows for a better representation of volatility persistence in financial data. Jumps and a leverage effect are also incorporated into the model and statistical properties are discussed. An empirical study on six financial time series shows that the FHMV process compares favorably to state-of-the-art volatility models in terms of in-sample fit and out-of-sample forecasting performance over time horizons ranging from one to one hundred days.

  • Generalized Sparse Additive Models

    Asad Haris · Jan 19, 2018

    Date: 2018-01-19

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    I will present a unified approach to the estimation of generalized sparse additive models in high dimensional regression problems. Our approach is based on combining structure-inducing and sparsity penalties in a single regression problem. It allows for the use of a large family of structure-inducing penalties: Those characterized by semi-norm constraints. This includes finite dimensional linear subspaces, sobolev and holder classes, classes with bounded total variation, among others. We give an efficient computational algorithm to fit this family of models that easily scales to thousands of observations and features. In addition we develop a framework for proving convergence bounds on these estimators; and show that our estimators converge at the minimax optimal rate under suitable conditions. We also compare the performance of existing methods in an empirical study and discuss directions for future work.

  • Modelling RNA stability for decoding the regulatory programs that drive human diseases

    Hamed Najafabadi · Jan 12, 2018

    Date: 2018-01-12

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    The key determinant of the identity and behaviour of the cell is gene regulation, i.e. which genes are active and which genes are inactive in a particular cell. One of the least understood aspects of gene regulation is RNA stability: genes produce RNA molecules to carry their genetic information – the more stable these RNA molecules are, the longer they can function within the cell, and the less stable they are, the more rapidly they are removed from the pool of active molecules. The cell can effectively switch the genes on and off by regulating RNA stability. However, we do not know which genes are regulated at the RNA stability level, and what factors affect their stability. The focus of our research is development of novel computational methods that enables the measurement of RNA stability and decay rate from functional genomics data, and inference of models that explain how human cells regulate RNA stability. We are particularly interested in how defects in regulation of RNA stability can lead to development and progression of various human diseases, such as cancer.

  • Fisher’s method revisited: set-based genetic association and interaction studies

    Lei Sun · Dec 1, 2017

    Date: 2017-12-01

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Fisher’s method, also known as Fisher’s combined probability test, is commonly used in meta-analyses to combine p-values from the same test applied to K independent samples to evaluate a common null hypothesis. Here we propose to use it to combine p-values from different tests applied to the same sample in two settings: when jointly analyzing multiple genetic variants in set-based genetic association studies, or when jointly capturing main and interaction effects in the presence of missing one of the interacting variables. In the first setting, we show that many existing methods (e.g. the so called burden test and SKAT) can be classified into a class of linear statistics and another class of quadratic statistics, where each class is powerful only in part of the high-dimensional parameter space. In the second setting, we show that the class of scale-tests for heteroscedasticity can be utilized to indirectly identify unspecified interaction effects, complementing the class of location-tests designed for detecting main effects only. In both settings, we show that the two classes of tests are asymptotically independent of each other under the global null hypothesis. Thus, we can evaluate the significance of the resulting Fisher’s test statistic using the chi-squared distribution with four degrees of freedom; this is a desirable feature for analyzing big data. In addition to analytical results, we provide empirical evidence to show that the new class of joint test is not only robust but can also have better power than the individual tests. This is based on join work with formal graduate students Andriy Derkach (Derkach et al. 2013, Genetic Epidemiology; Derkach et al. 2014, Statistical Science) and David Soave (Soave et al. 2015, The American Journal of Human Genetics; Soave and Sun 2017, Biometrics).

  • A log-linear time algorithm for constrained changepoint detection

    Toby Hocking · Nov 17, 2017

    Date: 2017-11-17

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Changepoint detection is a central problem in time series and genomic data. For some applications, it is natural to impose constraints on the directions of changes. One example is ChIP-seq data, for which adding an up-down constraint improves peak detection accuracy, but makes the optimization problem more complicated. In this talk I will explain how a recently proposed functional pruning algorithm can be generalized to solve such constrained changepoint detection problems. Our proposed log-linear time algorithm achieves state-of-the-art peak detection accuracy in a benchmark of several genomic data sets, and is orders of magnitude faster than our previous quadratic time algorithm. Our implementation is available as the PeakSegPDPA function in the PeakSegOptimal R package, https://cran.r-project.org/package=PeakSegOptimal

  • PAC-Bayesian Generalizations Bounds for Deep Neural Networks

    Daniel Roy · Nov 10, 2017

    Date: 2017-11-10

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    One of the defining properties of deep learning is that models are chosen to have many more parameters than available training data. In light of this capacity for overfitting, it is remarkable that simple algorithms like SGD reliably return solutions with low test error. One roadblock to explaining these phenomena in terms of implicit regularization, structural properties of the solution, and/or easiness of the data is that many learning bounds are quantitatively vacuous when applied to networks learned by SGD in this “deep learning” regime. Logically, in order to explain generalization, we need nonvacuous bounds. We return to an idea by Langford and Caruana (2001), who used PAC-Bayes bounds to compute nonvacuous numerical bounds on generalization error for stochastic two-layer two-hidden-unit neural networks via a sensitivity analysis. By optimizing the PAC-Bayes bound directly, we are able to extend their approach and obtain nonvacuous generalization bounds for deep stochastic neural network classifiers with millions of parameters trained on only tens of thousands of examples. We connect our findings to recent and old work on flat minima and MDL-based explanations of generalization. Time permitting, I will discuss recent work on computing even tighter generalization bounds associated with a learning algorithm introduced by Chaudhari et al. (2017), called Entropy-SGD. We show that Entropy-SGD indirectly optimizes a PAC-Bayes bound, but does so by optimizing the “prior” term, violating the hypothesis that the prior be independent of the data. We show how to fix this defect using differential privacy. The result is a new PAC-Bayes bound for data-dependent priors, which we show, up to some approximations, delivers even tighter generalization bounds. Joint work with Gintare Karolina Dziugaite, based on https://arxiv.org/abs/1703.11008