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DSI/Statistics Colloquium: Nikolaos Ignatiadis
11:30 am–12:30 pm DSI 105
Nikolaos Ignatiadis
DSI/Department of Statistics
University of Chicago
Title: Borrowing Strength in Multiple Testing with Compound p-values
Abstract: Many large-scale multiple testing problems in high-throughput biology involve thousands of units (e.g., genes or proteins) but only a small number of replicates per unit. A key observation in the microarray literature around the turn of the century was that standard t-tests may be nearly powerless in this setting. This motivated the development of methods such as the B-statistic (Lönnstedt and Speed, 2002), Significance Analysis of Microarrays (SAM; Tusher, Tibshirani and Chu, 2001), and limma (Smyth, 2004), which borrow information across units.
We study this type of borrowing across units through the lens of compound p-values. Unlike bona fide p-values, compound p-values need not be valid for each hypothesis separately, but instead satisfy an average superuniformity property across the null hypotheses. We first explain how compound p-values arise both from a nonparametric version of limma and from SAM. We then use the compound p-value perspective to construct a procedure that achieves the asymptotic power of the oracle Bayes rule in a sparse regime under the hierarchical model underlying the B-statistic and provides finite-sample frequentist control of the false discovery rate without requiring this hierarchical model to hold.
DSI/Statistics Colloquium: Frederic Koehler
11:30 am–12:30 pm DSI 105
Frederic Koehler
DSI/Department of Statistics
University of Chicago
Title: A Least-Squares Perspective on Ellipsoid Fitting
Abstract: Suppose we have n i.i.d. random vectors X_1,\ldots, X_n in d dimensions. How large can n be, as a function of d, such that there exists an ellipsoid interpolating all n points? Saunderson, Parrilo, and Willsky conjectured an explicit answer (n ~ d^2/4) for Gaussian data. Subsequently, many authors made rigorous progress on this question. We study a natural least-squares generalization of ellipsoid fitting, over a general class of data distributions, and solve its high-dimensional limit—- this proves the Gaussian conjecture as a special case. The solution combines in a nice way ideas from high-dimensional probability, statistical learning, and convex geometry + optimization.
Based on a joint work with Youngtak Sohn.
Statistics Colloquium: Kaizheng Wang
11:30 am–12:30 pm Jones 303
Kaizheng Wang
Department of Industrial Engineering and Operations Research/Data Science Institute
Columbia University
Title: Learning to Augment Statistical Inference with Generative Models
Abstract: Generative models can produce seemingly unlimited synthetic data, yet discrepancies between synthetic and real populations can introduce bias and undermine statistical conclusions. For a new task with scarce or no real data, how much synthetic data can be safely used? This talk develops a general framework that leverages historical tasks to calibrate synthetic-data augmentation and quantify the resulting uncertainty. When no real observations are available, the framework adaptively selects the synthetic sample size to achieve nominal average-case coverage. In the application to LLM-generated survey responses, this calibrated size can be interpreted as the number of human respondents the LLM is effectively worth, providing a measure of its simulation fidelity. More generally, when real observations are available, the augmentation scheme is characterized jointly by the number of synthetic observations and the weight assigned to each. We learn a size–weight frontier that identifies the largest synthetic contribution compatible with reliable uncertainty quantification. Together, these results show how generative models can strengthen statistical analysis when real data are limited.
Statistics Colloquium: Peter McCullagh
11:30 am–12:30 pm Jones 303
Peter McCullagh
Department of Statistics
University of Chicago
Title: TBA
Abstract: TBA
Statistics Colloquium: Jing Lei
11:30 am–12:30 pm Jones 303
Jing Lei
Carnegie Mellon University
Department of Statistics & Data Science
Title: TBA
Abstract: TBA
Statistics Colloquium: Michael Sobel
11:30 am–12:30 pm Jones 303
Michael Sobel
Columbia University
Department of Statistics
Title: TBA
Abstract: TBA
Statistics Colloquium: Bin Yu
11:30 am–12:30 pm
Bin Yu
Department of Statistics, Electrical Engineering and Computer Sciences, and Center for Computational Biology
University of California, Berkeley
Title: TBA
Abstract: TBA
Statistics Colloquium: Karl Rohe
11:30 am–12:30 pm
Karl Rohe
University of Wisconsin-Madison
Department of Statistics
Title: TBA
Abstract: TBA