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Autumn Semester 2020

Date / Time Speaker Title Location
18 September 2020
15:00-16:00 		Hongzhou Lin
MIT (Massachusetts Institute of Technology)
Event Details

Young Data Science Researcher Seminar Zurich

Title Stochastic Optimization with Non-stationary Noise
Speaker, Affiliation Hongzhou Lin, MIT (Massachusetts Institute of Technology)
Date, Time 18 September 2020, 15:00-16:00
Location
Abstract We investigate stochastic optimization problems under relaxed assumptions on the distribution of noise that are motivated by empirical observations in neural network training. Standard results on optimal convergence rates for stochastic optimization assume either there exists a uniform bound on the moments of the gradient noise, or that the noise decays as the algorithm progresses. These assumptions do not match the empirical behavior of optimization algorithms used in neural network training where the noise level in stochastic gradients could even increase with time. We address this behavior by studying convergence rates of stochastic gradient methods subject to changing second moment (or variance) of the stochastic oracle as the iterations progress. When the variation in the noise is known, we show that it is always beneficial to adapt the step-size and exploit the noise variability. When the noise statistics are unknown, we obtain similar improvements by developing an online estimator of the noise level, thereby recovering close variants of RMSProp. Consequently, our results reveal an important scenario where adaptive stepsize methods outperform SGD.
Stochastic Optimization with Non-stationary Noiseread_more
25 September 2020
17:00-18:00 		Raaz Dwivedi
UC Berkeley
Event Details

Young Data Science Researcher Seminar Zurich

Title StaDISC: Stable discovery of interpretable subgroups via calibration
Speaker, Affiliation Raaz Dwivedi, UC Berkeley
Date, Time 25 September 2020, 17:00-18:00
Location
Abstract In this talk, I will present some recent work where we introduce a novel methodology for Stable Discovery of Interpretable Subgroups via Calibration (StaDISC), with large heterogeneous treatment effects, for randomized experiments. Building on Yu and Kumbier's PCS framework, StaDISC was developed during our re-analysis of the 1999-2000 VIGOR study, an 8076 patient randomized controlled trial, that compared the risk of adverse events from a then newly approved drug, Rofecoxib (Vioxx), to that from an older drug Naproxen. On average, and in comparison to Naproxen, Vioxx was found to reduce the risk of gastrointestinal events but increase the risk of thrombotic cardiovascular events. Applying StaDISC, we fit 18 popular conditional average treatment effect (CATE) estimators for both outcomes and use calibration to demonstrate their poor global performance. However, we find that CATE methods are locally well-calibrated and stable, thereby enabling the identification of clinically interpretable patient groups with larger than (estimated) average treatment effects. External validation of the found subgroups provides further evidence for the promises of the proposed methodology. Based on joint work with Briton Park, Yan Shuo Tan, Mian Wei, Kevin Horgan, David Madigan, and Bin Yu arxiv preprint https://arxiv.org/abs/2008.10109 (in submission to international statistical review)
StaDISC: Stable discovery of interpretable subgroups via calibrationread_more
2 October 2020
15:00-16:00 		Mona Azadkia
ETH Zürich
Event Details

Young Data Science Researcher Seminar Zurich

Title A Simple Measure of Conditional Dependence
Speaker, Affiliation Mona Azadkia, ETH Zürich
Date, Time 2 October 2020, 15:00-16:00
Location
Abstract There are numerous problems where one needs to quantify the dependence between two random variables and how this dependence changes by conditioning on a third random variable. Correlated random variables might become independent when we observe a third random variable or two independent random variables might become dependent after conditioning on the third one. Thanks to the wide potential application range e.g., bioinformatics, economics, psychology, etc, finding efficient measures of conditional dependence has been an active area of research in many subareas of statistics and machine learning. However, the literature on measures of conditional dependence is not so large, especially in the non-parametric setting. We introduce two novel measures of conditional dependence and propose estimators based on i.i.d. samples. Using these statistics, we devise a new variable selection algorithm, called Feature Ordering by Conditional Independence (FOCI). FOCI is model-free with no tuning parameters and is provably consistent under sparsity assumptions. We provide a number of example application analyses to both synthetic and real datasets
A Simple Measure of Conditional Dependenceread_more
9 October 2020
15:00-16:00 		Alex Wein
NYU, New York University
Event Details

Young Data Science Researcher Seminar Zurich

Title Computational Barriers to Estimation from Low-Degree Polynomials
Speaker, Affiliation Alex Wein, NYU, New York University
Date, Time 9 October 2020, 15:00-16:00
Location
Abstract One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for such problems. Many leading algorithmic paradigms (such as spectral methods and approximate message passing) can be captured by low-degree polynomials, and thus, lower bounds against low-degree polynomials serve as evidence for computational hardness of statistical problems. Prior work has studied the power of low-degree polynomials for the detection (i.e. hypothesis testing) task. In this work, we extend these methods to address problems of estimating (i.e. recovering) the planted signal instead of merely detecting its presence. For a large class of "signal plus noise" problems, we give a user-friendly lower bound for the best possible mean squared error achievable by any degree-D polynomial. These are the first results to establish low-degree hardness of recovery problems for which the associated detection problem is easy. As applications, we study the planted submatrix and planted dense subgraph problems, resolving (in the low-degree framework) open problems about the computational complexity of recovery in both cases. Joint work with Tselil Schramm, available at: https://arxiv.org/abs/2008.02269
Computational Barriers to Estimation from Low-Degree Polynomialsread_more
16 October 2020
15:00-16:00 		Ramya Korlakai Vinayak
University of Wisconsin-Madison
Event Details

Young Data Science Researcher Seminar Zurich

Title Learning from Small Data
Speaker, Affiliation Ramya Korlakai Vinayak, University of Wisconsin-Madison
Date, Time 16 October 2020, 15:00-16:00
Location
Abstract Many scientific domains such as social sciences and epidemiology study heterogeneous populations (varying demographics) with only a few (small) observations available at the level of individuals. Limited observations prohibit accurate estimation of parameters of interest for any given individual. In this small data regime, the key question is, how accurately can we estimate the distribution of parameters over the population? In this talk, we investigate this fundamental and practically relevant problem of learning from a heterogeneous population with small data in the Binomial observation setting. While the maximum likelihood estimator (MLE) is widely used for this problem, its optimality and sample complexity in the small data regime were not well understood. We prove that the MLE is optimal even in the small data regime, resolving this problem open since the 1960s. We then use these results to construct new, optimal estimators for learning the change in the parameters over the population.
Learning from Small Dataread_more
23 October 2020
15:00-16:00 		Yuting Wei
Carnegie Mellon University
Event Details

Young Data Science Researcher Seminar Zurich

Title Reliable hypothesis testing paradigms in high dimensions
Speaker, Affiliation Yuting Wei, Carnegie Mellon University
Date, Time 23 October 2020, 15:00-16:00
Location
Abstract Modern scientific discovery and decision making require the development of trustworthy and informative inferential procedures, which are particularly challenging when coping with high-dimensional data. This talk presents two vignettes on the theme of reliable high-dimensional inference. The first vignette considers performing inference based on the Lasso estimator when the number of covariates is of the same order or larger than the number of observations. Classical asymptotic statistics theory fails due to two fundamental reasons: (1) The regularized risk is non-smooth; (2) The discrepancy between the estimator and the true parameter vector cannot be neglected. We pin down the distribution of the Lasso, as well as its debiased version, under a broad class of Gaussian correlated designs with non-singular covariance structure. Our findings suggest that a careful degree-of-freedom correction is crucial for computing valid confidence intervals in this challenging regime. The second vignette investigates the Model-X knockoffs framework --- a general procedure that can leverage any feature importance measure to produce a variable selection algorithm. Model-X knockoffs rely on the construction of synthetic random variables and is, therefore, random. We propose a method for derandomizing --- and hence stabilizing --- model-X knockoffs. By aggregating the selection results across multiple runs of the knockoffs algorithm, our method provides stable decisions without compromising statistical power. Our approach, when applied to the multi-stage GWAS of prostate cancer, reports locations on the genome that have been replicated with other studies. The first vignette is based on joint work with Michael Celentano and Andrea Montanari, whereas the second one is based on joint work with Zhimei Ren and Emmanuel Candes.
Reliable hypothesis testing paradigms in high dimensionsread_more
30 October 2020
15:00-16:00 		Merle Behr
University of California, Berkeley
Event Details

Young Data Science Researcher Seminar Zurich

Title Learning Compositional Structures
Speaker, Affiliation Merle Behr, University of California, Berkeley
Date, Time 30 October 2020, 15:00-16:00
Location
Abstract Many data problems, in particular in biogenetics, often come with a highly complex underlying structure. This often makes it difficult to extract interpretable information. In this talk we want to demonstrate that often these complex structures are well approximated by a composition of a few simple parts, which provides very descriptive insights into the underlying data generating process. We demonstrate this with two examples. In the first example, the single components are finite alphabet vectors (e.g., binary components), which encode some discrete information. For instance, in genetics a binary vector of length n can encode whether or not a mutation (e.g., a SNP) is present at location i = 1,…,n in the genome. On the population level studying genetic variations is often highly complex, as various groups of mutations are present simultaneously. However, in many settings a population might be well approximated by a composition of a few dominant groups. Examples are Evolve and Resequence experiments where the outer supply of genetic variation is limited and thus, over time, only a few haplotypes survive. Similarly, in a cancer tumor, often only a few competing groups of cancer cells (clones) come out on top. In the second example, the single components relate to separate branches of a tree structure. Tree structures, showing hierarchical relationships between samples, are ubiquitous in genomic and biomedical sciences. A common question in many studies is whether there is an association between a response variable and the latent group structure represented by the tree. Such a relation can be highly complex, in general. However, often it is well approximated by a simple composition of relations associated with a few branches of the tree. For both of these examples we first study theoretical aspects of the underlying compositional structure, such as identifiability of single components and optimal statistical procedures under probabilistic data models. Based on this, we find insights into practical aspects of the problem, namely how to actually recover such components from data.
Learning Compositional Structuresread_more
6 November 2020
15:00-16:00 		Eugene Katsevich
University of Pennsylvania
Event Details

Young Data Science Researcher Seminar Zurich

Title Finite-sample optimality and large-sample power analysis of the conditional randomization test
Speaker, Affiliation Eugene Katsevich, University of Pennsylvania
Date, Time 6 November 2020, 15:00-16:00
Location
Abstract For testing conditional independence of a response Y and a predictor X given covariates Z, the recently introduced model-X (MX) framework has been the subject of active methodological research, especially in the context of MX knockoffs and their successful application to genome-wide association studies. In this talk, we study the power of conditional independence testing under MX, focusing our analysis on the conditional randomization test (CRT). The validity of the CRT conditionally on Y,Z allows us to view it as a test of a point null hypothesis involving the conditional distribution of X, from which we can use the Neyman-Pearson lemma to derive the most powerful CRT statistic against a point alternative. We obtain an analogous result for MX knockoffs as well. Next, we derive expressions for the power of the CRT against local semiparametric alternatives, establishing a direct link between the performance of the power of the CRT and the performance of the machine learning method on which it is based. If time permits, we will discuss a recent computational acceleration of the CRT that permits its application to large-scale datasets.
Finite-sample optimality and large-sample power analysis of the conditional randomization testread_more
13 November 2020
15:00-16:00 		Nabarun Deb
Columbia University
Event Details

Young Data Science Researcher Seminar Zurich

Title Measuring Association on Topological Spaces Using Kernels and Geometric Graphs
Speaker, Affiliation Nabarun Deb, Columbia University
Date, Time 13 November 2020, 15:00-16:00
Location
Abstract In this work, we propose a class of simple, nonparametric, yet interpretable measures of association between two random variables X and Y taking values in general topological spaces. These nonparametric measures — defined using the theory of reproducing kernel Hilbert spaces — capture the strength of dependence between X and Y and have the property that they are 0 if and only if the variables are independent and 1 if and only if one variable is a measurable function of the other. Further, these population measures can be consistently estimated using the general framework of geometric graphs which include k-nearest neighbor graphs and minimum spanning trees. Moreover, a sub-class of these estimators are also shown to adapt to the intrinsic dimensionality of the underlying distribution. Some of these empirical measures can also be computed in near-linear time. If X and Y are independent, these empirical measures (properly normalized) have a standard normal limiting distribution and hence, can be readily used to test for independence. In fact, as far as we are aware, these are the only procedures that possess all the above mentioned desirable properties. The correlation coefficient proposed in Dette et al. [31], Chatterjee [22], and Azadkia and Chatterjee [7] can be seen as a special case of this general class of measures. If time permits, I will also describe how the same ideas can be effectively used to measure the strength of conditional dependence. The talk is based on this paper https://arxiv.org/abs/2010.01768.
Measuring Association on Topological Spaces Using Kernels and Geometric Graphsread_more
20 November 2020
15:00-16:00 		Martin Wahl
HU Berlin
Event Details

Young Data Science Researcher Seminar Zurich

Title Upper and lower bounds for the estimation of principal components
Speaker, Affiliation Martin Wahl, HU Berlin
Date, Time 20 November 2020, 15:00-16:00
Location
Abstract In settings where the number of observations is comparable to the dimension, principal component analysis (PCA) reveals some unexpected phenomena, ranging from eigenprojector inconsistency to eigenvalue upward bias. While such high-dimensional phenomena are now well understood in the spiked covariance model, the goal of this talk is to discuss some extensions for the case of PCA in infinite dimensions. In particular, we will introduce a new perturbation-theoretic framework that will allow us to characterize the behavior of eigenvalues and eigenprojectors of empirical covariance operators by the so-called ``relative ranks''. If time permits, we will also present some corresponding minimax lower bounds for the estimation of eigenprojectors. These are obtained by a van Trees inequality for invariant statistical models.
Upper and lower bounds for the estimation of principal componentsread_more
4 December 2020
15:00-16:00 		Zhou Fan
Yale University
Event Details

Young Data Science Researcher Seminar Zurich

Title Empirical Bayes and Approximate Message Passing algorithms for PCA in high dimensions
Speaker, Affiliation Zhou Fan, Yale University
Date, Time 4 December 2020, 15:00-16:00
Location
Abstract This talk will be divided into two halves. In a first more applied half, I will describe a new empirical Bayes procedure for principal components analysis in high dimensions, which aims to learn a prior distribution for the PCs from the observed data. Its ideas are based around the Kiefer-Wolfowitz NPMLE, some basic results in asymptotic random matrix theory, and Approximate Message Passing (AMP) algorithms for Bayesian inference. I will explain the interplay between these ideas and demonstrate the method on several genetics examples. In a second more theoretical half, motivated by this application, I will then describe a general extension of AMP algorithms to a class of rotationally invariant matrices. The usual bias correction and state evolution in AMP are replaced by forms involving the free cumulants of the spectral law. I hope to explain the main ideas behind this algorithm, and connect this back to the PCA application. This is joint work with Xinyi Zhong and Chang Su.
Empirical Bayes and Approximate Message Passing algorithms for PCA in high dimensionsread_more
11 December 2020
15:00-16:00 		Kweku Abraham
Université Paris-Sud
Event Details

Young Data Science Researcher Seminar Zurich

Title Optimal false discovery rate control of a nonparametric hidden Markov model multiple testing procedure
Speaker, Affiliation Kweku Abraham, Université Paris-Sud
Date, Time 11 December 2020, 15:00-16:00
Location
Abstract Multiple testing has become a very important statistical problem in the age of high-dimensional data sets. Abstractly, the goal is as follows: Given measurements of very many covariates (for example, the nucleotides forming someones DNA), return those covariates which are predictive of some output data (such as health outcomes). A typical design aim for the statistician is to give a procedure with controlled "size", in that the so-called False Discovery Rate (FDR) is controlled at some target level, while maximising the number of true discoveries. I will explain that a commonly used method based on posterior ("smoothing") probabilities achieves this goal when the covariates have a Markov dependence structure.
Optimal false discovery rate control of a nonparametric hidden Markov model multiple testing procedureread_more

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