McGill Statistics Seminar

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

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.

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.

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.

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).

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

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

Date: 2017-11-03

Time: 15:30-16:30

Location: BURN 1205

Abstract:

In this talk, I will outline how to do (Bayesian) statistics. I will focus particularly on the things that need to be done before you see data, including prior specification and checking that your inference algorithm actually works.

Speaker

Daniel Simpson is an Assistant Professor in the Department of Statistical Sciences, University of Toronto

Date: 2017-10-27

Time: 15:30-16:30

Location: BURN 1205

Abstract:

In many current applications, scientists can easily measure a very large number of variables (for example, hundreds of protein levels), some of which are expected be useful to explain or predict a specific response variable of interest. These potential explanatory variables are most likely to contain redundant or irrelevant information, and in many cases, their quality and reliability may be suspect. We developed two penalized robust regression estimators that can be used to identify a useful subset of explanatory variables to predict the response, while protecting the resulting estimator against possible aberrant observations in the data set. Using an elastic net penalty, the proposed estimator can be used to select variables, even in cases with more variables than observations or when many of the candidate explanatory variables are correlated. In this talk, I will present the new estimator and an algorithm to compute it. I will also illustrate its performance in a simulation study and a real data set. This is joint work with Professor Matias Salibian-Barrera, my PhD student David Kepplinger, and my PDF Ezequiel Smuggler.

Date: 2017-10-20

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Statistical optimization has generated quite some interest recently. It refers to the case where hidden and local convexity can be discovered in most cases for nonconvex problems, making polynomial algorithms possible. It relies on a careful analysis of the geometry near global optima. In this talk, I will explore this issue by focusing on sparse regression problems in high dimensions. A computational framework named iterative local adaptive majorize-minimization (I-LAMM) will be proposed to simultaneously control algorithmic complexity and statistical error. I-LAMM effectively turns the nonconvex penalized regression problem into a series of convex programs by utilizing the locally strong convexity of the problem when restricting the solution set in an L_1 cone. Computationally, we establish a phase transition phenomenon: it enjoys a linear rate of convergence after a sub-linear burn-in. Statistically, it provides solutions with optimal statistical errors. Extensions to robust regression will be discussed.