Related papers: Some remarks on the Gram-Schmidt walk algorithm an…
When solving consensus optimization problems over a graph, there is often an explicit characterization of the convergence rate of Gradient Descent (GD) using the spectrum of the graph Laplacian. The same type of problems under the…
We obtain an improved finite-sample guarantee on the linear convergence of stochastic gradient descent for smooth and strongly convex objectives, improving from a quadratic dependence on the conditioning $(L/\mu)^2$ (where $L$ is a bound on…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
The random order graph streaming model has received significant attention recently, with problems such as matching size estimation, component counting, and the evaluation of bounded degree constant query testable properties shown to admit…
This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…
We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…
The Metropolis-Hastings algorithm has been extensively studied in the estimation and simulation literature, with most prior work focusing on convergence behavior and asymptotic theory. However, its covariance structure-an important…
Motivated by Bayesian inference with highly informative data we analyze the performance of random walk-like Metropolis-Hastings algorithms for approximate sampling of increasingly concentrating target distributions. We focus on Gaussian…
Consider the random walk $G_n : = g_n \ldots g_1$, $n \geq 1$, where $(g_n)_{n\geq 1}$ is a sequence of independent and identically distributed random elements with law $\mu$ on the general linear group ${\rm GL}(V)$ with $V=\mathbb R^d$.…
We obtain Gaussian upper and lower bounds on the transition density q_t(x,y) of the continuous time simple random walk on a supercritical percolation cluster C_{\infty} in the Euclidean lattice. The bounds, analogous to Aronsen's bounds for…
In this work, we propose Random Walk-steered Majority Undersampling (RWMaU), which undersamples the majority points of a class imbalanced dataset, in order to balance the classes. Rather than marking the majority points which belong to the…
We study the problem of detecting a change in the mean of one-dimensional Gaussian process data. This problem is investigated in the setting of increasing domain (customarily employed in time series analysis) and in the setting of fixed…
We propose a method for zeroth order stochastic convex optimization that attains the suboptimality rate of $\tilde{\mathcal{O}}(n^{7}T^{-1/2})$ after $T$ queries for a convex bounded function $f:{\mathbb R}^n\to{\mathbb R}$. The method is…
We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on…
We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the $1/\sqrt{t}$…
With the growing interest in quantum machine learning, the perceptron -- a fundamental building block in traditional machine learning -- has emerged as a valuable model for exploring quantum advantages. Two quantum perceptron algorithms…
We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to…
Given a connected graph $G$ with some subset of its vertices excited and a fixed target vertex, in the geodesic-biased random walk on $G$, a random walker moves as follows: from an unexcited vertex, she moves to a uniformly random…
We investigate random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy Cramer's condition. We prove moderate deviation principles in dimensions two and larger, covering…
We study lower bounds for the problem of approximating a one dimensional distribution given (noisy) measurements of its moments. We show that there are distributions on $[-1,1]$ that cannot be approximated to accuracy $\epsilon$ in…