Topological data analysis (TDA) can broadly be described as a collection of data analysis
methods that find structure in data. These methods include clustering, manifold estimation …

This paper is an attempt to bridge the conceptual gaps between researchers working on the
two widely used approaches based on positive definite kernels: Bayesian learning or …

The Poisson process, a core object in modern probability, enjoys a richer theory than is
sometimes appreciated. This volume develops the theory in the setting of a general abstract …

High-dimensional probability offers insight into the behavior of random vectors, random
matrices, random subspaces, and objects used to quantify uncertainty in high dimensions …

After a decade of periodic truss-, plate-, and shell-based architectures having dominated the
design of metamaterials, we introduce the non-periodic class of spinodoid topologies …

Gradient Descent Only Converges to Minimizers Page 1 JMLR: Workshop and Conference
Proceedings vol 49:1–12, 2016 Gradient Descent Only Converges to Minimizers Jason D. Lee …

We present a two-scale topology optimization framework for the design of macroscopic
bodies with an optimized elastic response, which is achieved by means of a spatially-variant …

We establish that first-order methods avoid strict saddle points for almost all initializations.
Our results apply to a wide variety of first-order methods, including (manifold) gradient …

Abstract Background The Republic of Georgia (Sakartvelo in Georgian language) is part of
the Caucasus biodiversity hotspot, and human agricultural plant use dates bat at least 6000 …

We study statistical inference and distributionally robust solution methods for stochastic
optimization problems, focusing on confidence intervals for optimal values and solutions that …