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Title: Distribution-鈥媐ree inference for regression: discrete, continuous, and in between.

In data analysis problems where we are not able to rely on distributional assumptions, what types of inference guarantees can still be obtained? Many popular methods, such as holdout methods, cross-validation methods, and conformal prediction, are able to provide distribution-free guarantees for predictive inference, but the problem of providing inference for the underlying regression function (for example, inference on the conditional mean E[Y|X]) is more challenging. If X takes only a small number of possible values, then inference on E[Y|X] is trivial to achieve. At the other extreme, if the features X are continuously distributed, we show that any confidence interval for E[Y|X] must have non-vanishing width, even as sample size tends to infinity - this is true regardless of smoothness properties or other desirable features of the underlying distribution. In between these two extremes, we find several distinct regimes - in particular, it is possible for distribution-free confidence intervals to have vanishing width if and only if the effective support size of the distribution ofXis smaller than the square of the sample size.

This work is joint with Yonghoon Lee.

Dr. Barber is the Louis Block Professor of statistics at the University of Chicago. Before starting at U of C, she worked in the Department of Statistics at Stanford University, supervised by Dr. Emmanuel Candes. She was awarded the 2020 COPSS Presidents' Award for her fundamental contributions to statistical sparsity and selective inference in high-dimensional problems; for the creative and novel knockoff filter to cope with correlated coefficients; for contributions to compressed sensing, the jackknife, and conformal predictive inference; and for the encouragement and training of graduate and undergraduate students.

Her research interests are in developing and analyzing estimation, inference, and optimization tools for structured high-dimensional data problems such as sparse regression, sparse nonparametric models, and low-rank models. She also collaborate on modeling and optimization problems in image reconstruction for medical imaging.

McGill Statistics Seminar schedule:

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