Stochastics and Statistics Seminar

Abstract: Two of the fundamental problems in non-parametric statistical inference are goodness-of-fit and two-sample testing. These two problems have been extensively studied and several multivariate tests have been proposed over the last thirty years, many of which are based on geometric graphs. These include, among several others, the celebrated Friedman-Rafsky two-sample test based on the minimal spanning tree and the K-nearest neighbor graphs, and the Bickel-Breiman spacings tests for goodness-of-fit. These tests are asymptotically distribution-free, universally consistent, and computationally efficient…

Abstract: For many causal effect parameters of interest, doubly robust machine learning (DRML) estimators ψ̂ 1 are the state-of-the-art, incorporating the good prediction performance of machine learning; the decreased bias of doubly robust estimators; and the analytic tractability and bias reduction of sample splitting with cross fitting. Nonetheless, even in the absence of confounding by unmeasured factors, the nominal (1−α) Wald confidence interval ψ̂ 1±zα/2ˆ may still undercover even in large samples, because the bias of ψ̂ 1 may be of the same…

Abstract: We consider sequential prediction with expert advice when data are generated from distributions varying arbitrarily within an unknown constraint set. We quantify relaxations of the classical i.i.d. assumption in terms of these constraint sets, with i.i.d. sequences at one extreme and adversarial mechanisms at the other. The Hedge algorithm, long known to be minimax optimal in the adversarial regime, was recently shown to be minimax optimal for i.i.d. data. We show that Hedge with deterministic learning rates is suboptimal…

Abstract: Mainstream machine learning, despite its recent successes, has a serious drawback: while its state-of-the-art algorithms often produce excellent predictions, they do not provide measures of their accuracy and reliability that would be both practically useful and provably valid. Conformal prediction adapts rank tests, popular in nonparametric statistics, to testing the IID assumption (the observations being independent and identically distributed). This gives us practical measures, provably valid under the IID assumption, of the accuracy and reliability of predictions produced by…

Abstract: The magnitude of the weights of a neural network is a fundamental measure of complexity that plays a crucial role in the study of implicit and explicit regularization. For example, in recent work, gradient descent updates in overparameterized models asymptotically lead to solutions that implicitly minimize the ell_2 norm of the parameters of the model, resulting in an inductive bias that is highly architecture dependent. To investigate the properties of learned functions, it is natural to consider a function…

Abstract:  Sequential Multiple Assignment Randomized Trials (SMARTs) are considered the gold standard for estimation and evaluation of treatment regimes. SMARTs are typically sized to ensure sufficient power for a simple comparison, e.g., the comparison of two fixed treatment sequences. Estimation of an optimal treatment regime is conducted as part of a secondary and hypothesis-generating analysis with formal evaluation of the estimated optimal regime deferred to a follow-up trial. However, running a follow-up trial to evaluate an estimated optimal treatment regime…

Abstract: Prioritizing likely causal genes from genome-wide association studies (GWAS) is a fundamental problem. There are many methods for GWAS gene prioritization, including methods that map candidate SNPs to their target genes and methods that leverage patterns of enrichment from across the genome. In this talk, I will introduce a new method for leveraging genome-wide patterns of enrichment to prioritize genes at GWAS loci, incorporating information about genes from many sources. I will then discuss the problem of benchmarking gene prioritization methods,…

Abstract: Many areas of the physical, engineering and biological sciences make extensive use of computer simulators to model complex systems. Confidence sets and hypothesis testing are the hallmarks of statistical inference, but classical methods are poorly suited for scientific applications involving complex simulators without a tractable likelihood. Recently, many techniques have been introduced that learn a surrogate likelihood using forward-simulated data, but these methods do not guarantee frequentist confidence sets and tests with nominal coverage and Type I error control,…

Title: Interpolation and learning with scale dependent kernels Abstract:  We study the learning properties of nonparametric ridge-less least squares. In particular, we consider the common case of estimators defined by scale dependent (Matern) kernels, and focus on the role scale and smoothness. These estimators interpolate the data and the scale can be shown to control their stability to noise and sampling.  Larger scales, corresponding to smoother functions, improve stability with respect to sampling. However, smaller scales, corresponding to more complex functions,…

Abstract:  Self-supervised learning is an increasingly popular approach for learning representations of data that can be used for downstream representation tasks. A practical advantage of self-supervised learning is that it can be used on unlabeled data. However, even when labels are available, self-supervised learning can be competitive with the more "traditional" approach of supervised learning. In this talk we consider "self supervised + simple classifier (SSS)" algorithms, which are obtained by first learning a self-supervised classifier on data, and then…