Related papers: Things we can learn by considering random locally …

This paper is a survey of methods for solving smooth (strongly) monotone stochastic variational inequalities. To begin with, we give the deterministic foundation from which the stochastic methods eventually evolved. Then we review methods…

In this paper, we study Markovian random iterations of maps on standard measurable spaces. We establish a one-to-one correspondence between stationary measures and a certain class of invariant measures of a Markovian random iteration,…

We develop a validated numerical procedure for continuation of local stable/unstable manifold patches attached to equilibrium solutions of ordinary differential equations. The procedure has two steps. First we compute an accurate high order…

In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…

We give a new proof for the local existence of a smooth isometric embedding of a smooth $3$-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into $6$-dimensional Euclidean space. Our proof avoids the sophisticated…

Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…

Stochastic rounding (SR) is a probabilistic method used to round numbers to floating-point and fixed-point representations. In length $n$ summation, the worst-case error of SR grows as $\sqrt{n}$ with high probability, unlike for standard…

Quite often real-world networks can be thought of as being symmetric, in the abstract sense that vertices can be found to have similar or equivalent structural roles. However, traditional measures of symmetry in graphs are based on their…

Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…

Due to the limited number of bits in floating-point or fixed-point arithmetic, rounding is a necessary step in many computations. Although rounding methods can be tailored for different applications, round-off errors are generally…

We construct several new classes of isospectral manifolds with different local geometries. After reviewing a theorem by Carolyn Gordon on isospectral torus bundles and presenting certain useful specialized versions (Chapter 1) we apply…

Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…

We study the problem of supervised learning for both binary and multiclass classification from a unified geometric perspective. In particular, we propose a geometric regularization technique to find the submanifold corresponding to a robust…

We initiate the study of differentially private hypothesis testing in the local-model, under both the standard (symmetric) randomized-response mechanism (Warner, 1965, Kasiviswanathan et al, 2008) and the newer (non-symmetric) mechanisms…

This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…

Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…

Partial Observability -- where agents can only observe partial information about the true underlying state of the system -- is ubiquitous in real-world applications of Reinforcement Learning (RL). Theoretically, learning a near-optimal…

Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…

Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…