We study the problem of robust subspace recovery (RSR) in the presence of adversarial outliers. That is, we seek a subspace that contains a large portion of a dataset when some fraction of the data points are arbitrarily corrupted. We first examine a theoretical estimator that is intractable to calculate and use it to derive information-theoreti...
Creator:
Maunu, Tyler (Massachusetts Institute of Technology)
Created:
2019-06-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We introduce the jackknife+, a novel method for constructing predictive confidence intervals that is robust to the distribution of the data. The jackknife+ modifies the well-known jackknife (leave-one-out cross-validation) to account for the variability in the fitted regression function when we subsample the training data. Assuming exchangeable ...
Creator:
Barber, Rina (University of Chicago)
Created:
2019-06-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The replication of DNA requires the assistance of topology changing enzymes called topoisomerases. Efforts to discover the mechanisms by which various enzymes act on DNA has focused attention on questions for which geometrical and topological considerations provide insights as well as raising new questions. In this first lecture, we will explore...
Creator:
Millett, Kenneth (University of California, Santa Barbara)
Created:
2019-06-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We consider the problem of estimating the common mean of univariate data, when independent samples are drawn from non-identical symmetric, unimodal distributions. This captures the setting where all samples are Gaussian with different unknown variances. We propose an estimator that adapts to the level of heterogeneity in the data, achieving near...
Creator:
Loh, Po-Ling (University of Wisconsin, Madison)
Created:
2019-06-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts, or unmodeled temporal effects. We develop and analyze a distributionally robust stochastic optimization (DRO) framework that learns a model that provides g...
Creator:
Duchi, John (Stanford University)
Created:
2019-06-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Knots can be distinguished via invariants. Invariants measure different aspects of knottedness. Crossing number, bridge number, tunnel number and unknotting number provide distinct insights. Moreover, the behavior of these invariants under connected sum deserves closer scrutiny.
Creator:
Schultens, Jennifer (University of California, Davis)
Created:
2019-06-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Fitting a model to a collection of observations is one of the quintessential questions in statistics. The standard assumption is that the data was generated by a model of a given type (e.g., a mixture model). This simplifying assumption is at best only approximately valid, as real datasets are typically exposed to some source of contamination. H...
Creator:
Diakonikolas, Ilias (University of Southern California)
Created:
2019-06-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We begin with the generalization of electrostatic energy of charged knots, where we come across the difficulty of divergent integrals. Two kinds of regularization will be introduced, Hadamard regularization and the regularization via analytic continuation, both from the theory of generalized functions.
Creator:
O'Hara, Jun (Chiba University)
Created:
2019-06-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
