Related papers: A Systematic Martingale Construction with Applicat…
This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
By making use of martingale representations, we derive the asymptotic normality of particle filters in hidden Markov models and a relatively simple formula for their asymptotic variances. Although repeated resamplings result in complicated…
Disentanglement via mechanism sparsity was introduced recently as a principled approach to extract latent factors without supervision when the causal graph relating them in time is sparse, and/or when actions are observed and affect them…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or…
Orthogonal arrays are arguably one of the most fascinating and important statistical tools for efficient data collection. They have a simple, natural definition, desirable properties when used as fractional factorials, and a rich and…
We present a few techniques for proving $L^p$ estimates for martingales. Basic applications to It\^o integration and rough paths are included.
The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the…
We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several properties that have been out of reach before: generating…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
We develop a martingale approximation framework yielding quantitative maximal large deviations estimates for invertible dynamical systems. From suitable decay of correlations, we deduce these estimates and, as an application, we obtain…
We examine a random model consisting of objects with positive weights and evolving in discrete time steps, which generalizes certain random graph models. We prove almost sure convergence for the weight distribution and show scale-free…
Berman's inequality is the key for establishing asymptotic properties of maxima of Gaussian random sequences and supremum of Gaussian random fields. This contribution shows that, asymptotically an extended version of Berman's inequality can…
This article proposes a novel test for the martingale difference hypothesis based on the martingale difference divergence function, a recently developed dependence measure suitable for measuring the degree of conditional mean dependence of…
In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and…
We propose a novel approach in noncommutative probability, which can be regarded as an analogue of good-$\lambda$ inequalities from the classical case due to Burkholder and Gundy (Acta Math {\bf124}: 249-304,1970). This resolves a…
Gaussian Processes face two primary challenges: constructing models for large datasets and selecting the optimal model. This master's thesis tackles these challenges in the low-dimensional case. We examine recent convergence results to…
In this paper we provide necessary and sufficient conditions for the mean square approximation of a random field with an ortho-martingale. The conditions are formulated in terms of projective criteria. Applications are given to linear and…