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.
Daniel Simpson is an Assistant Professor in the Department of Statistical Sciences, University of Toronto
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.
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.
In various applications, evaluating spatial risks (such as floods, heatwaves or storms) is a key problem. The aim of this talk is to make use of extreme value theory and max-stable processes to provide quantitative answers to this issue. A review of the literature will be provided, as well as a wide comparative study based on a simulation design mimicking daily rainfall in France. This is a joint work with Cécile Mercadier (Université Claude-Bernard Lyon 1 (UCBL)) and Quentin Sebille (UCBL).
We study the problem of nonparametric dependence detection. Many existing methods suffer severe power loss due to non-uniform consistency, which we illustrate with a paradox. To avoid such power loss, we approach the nonparametric test of independence through the new framework of binary expansion statistics (BEStat) and binary expansion testing (BET), which examine dependence through a filtration induced by marginal binary expansions. Through a novel decomposition of the likelihood of contingency tables whose sizes are powers of 2, we show that the interactions of binary variables in the filtration are complete sufficient statistics for dependence. These interactions are also pairwise independent under the null. By utilizing these interactions, the BET avoids the problem of non-uniform consistency and improves upon a wide class of commonly used methods (a) by achieving the optimal rate in sample complexity and (b) by providing clear interpretations of global and local relationships upon rejection of independence. The binary expansion approach also connects the test statistics with the current computing system to allow efficient bitwise implementation. We illustrate the BET by a study of the distribution of stars in the night sky and by an exploratory data analysis of the TCGA breast cancer data.
The demand for time series forecasting at Google has grown rapidly along with the company since its founding. Initially, the various business and engineering needs led to a multitude of forecasting approaches, most reliant on direct analyst support. The volume and variety of the approaches, and in some cases their inconsistency, called out for an attempt to unify, automate, and extend forecasting methods, and to distribute the results via tools that could be deployed reliably across the company. That is, for an attempt to develop methods and tools that would facilitate accurate large-scale time series forecasting at Google. We were part of a team of data scientists in Search Infrastructure at Google that took on the task of developing robust and automatic large-scale time series forecasting for our organization. In this talk, we recount how we approached the task, describing initial stakeholder needs, the business and engineering contexts in which the challenge arose, and theoretical and pragmatic choices we made to implement our solution. We describe our general forecasting framework, offer details on various tractable subproblems into which we decomposed our overall forecasting task, and provide an example of our forecasting routine applied to publicly available Turkish Electricity data.
A central goal of population genetics is the inference of the biological, evolutionary and demographic forces that shaped human diversity. Large-scale sequencing experiments provide fantastic opportunities to learn about human history and biology if we can overcome computational and statistical challenges. I will discuss how simple mid-century statistical approaches, such as the jackknife and Kolmogorov equations, can be combined in unexpected ways to solve partial differential equations, optimize genomic study design, and learn about the spread of modern humans since our common African origins.
In modern scientific research, massive datasets with huge numbers of observations are frequently encountered. To facilitate the computational process, a divide-and-conquer scheme is often used for the analysis of big data. In such a strategy, a full dataset is first split into several manageable segments; the final output is then aggregated from the individual outputs of the segments. Despite its popularity in practice, it remains largely unknown that whether such a distributive strategy provides valid theoretical inferences to the original data; if so, how efficient does it work? In this talk, I address these fundamental issues for the non-parametric distributed kernel regression, where accurate prediction is the main learning task. I will begin with the naive simple averaging algorithm and then talk about an improved approach via ADMM. The promising preference of these methods is supported by both simulation and real data examples.
Sample size determination problem is an important task in the planning of clinical trials. The problem may be formulated formally in statistical terms. The most frequently used methods are based on the required size, and power of the trial for a specified treatment effect. In contrast to the Bayesian decision-theoretic approach, there is no explicit balancing of the cost of a possible increase in the size of the trial against the benefit of the more accurate information which it would give. In this talk a fully Bayesian approach to the sample size determination problem is discussed. This approach treats the problem as a decision problem and employs a utility function to find the optimal sample size of a trial. Furthermore, we assume that a regulatory authority, which is deciding on whether or not to grant a licence to a new treatment, uses a frequentist approach. The optimal sample size for the trial is then found by maximising the expected net benefit, which is the expected benefit of subsequent use of the new treatment minus the cost of the trial.
The immune system does a lot more than killing “foreign” invaders. It’s a powerful sensory system that can detect stress levels, infections, wounds, and even cancer tumors. However, due to the complex interplay between different cell types and signaling pathways, the amount of data produced to characterize all different aspects of the immune system (tens of thousands of genes measured and hundreds of millions of cells, just from a single patient) completely overwhelms existing bioinformatics tools. My laboratory specializes in the development of machine learning techniques that address the unique challenges of high-throughput single-cell immunology. Sharing our lab space with a clinical and an immunological research laboratory, my students and fellows are directly exposed to the real-world challenges and opportunities of bringing machine learning and immunology to the (literal) bedside.