Related papers: Stochastic approximation on non-compact measure sp…
Given the widespread use of lossless compression algorithms to approximate algorithmic (Kolmogorov-Chaitin) complexity, and that lossless compression algorithms fall short at characterizing patterns other than statistical ones not different…
We investigate the numerical approximation of integrals over $\mathbb{R}^d$ equipped with the standard Gaussian measure $\gamma$ for integrands belonging to the Gaussian-weighted Sobolev spaces $W^\alpha_p(\mathbb{R}^d, \gamma)$ of mixed…
We introduce a notion of vague convergence for random marked metric measure spaces. Our main result shows that convergence of the moments of order $k \ge 1$ of a random marked metric measure space is sufficient to obtain its vague…
In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…
Let $\mathscr{P}(E)$ be the space of probability measures on a measurable space $(E,\mathcal{E})$. In this paper we introduce a class of nonlinear Markov chain Monte Carlo (MCMC) methods for simulating from a probability measure…
We show that for several variations of partially observable Markov decision processes, polynomial-time algorithms for finding control policies are unlikely to or simply don't have guarantees of finding policies within a constant factor or a…
The Friedman's urn model is a popular urn model which is widely used in many disciplines. In particular, it is extensively used in treatment allocation schemes in clinical trials. In this paper, we prove that both the urn composition…
We prove a central limit theorem applicable to one dimensional stochastic approximation algorithms that converge to a point where the error terms of the algorithm do not vanish. We show how this applies to a certain class of these…
We construct a family of non-parametric (infinite-dimensional) manifolds of finite measures on $R^d$. The manifolds are modelled on a variety of weighted Sobolev spaces, including Hilbert-Sobolev spaces and mixed-norm spaces. Each supports…
This article presents a novel numerically tractable technique for synthesizing Lyapunov functions for equilibria of nonlinear vector fields. In broad strokes, corresponding to an isolated equilibrium point of a given vector field, a…
Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling of physical phenomena to computational methods. A PDMP is…
Mean-field models approximate large stochastic systems by simpler differential equations that are supposed to approximate the mean of the larger system. It is generally assumed that as the stochastic systems get larger (i.e., more people or…
We discuss the statistical properties of a recently introduced unbiased stochastic approximation to the score equations for maximum likelihood calculation for Gaussian processes. Under certain conditions, including bounded condition number…
This paper studies a structured compound stochastic program (SP) involving multiple expectations coupled by nonconvex and nonsmooth functions. We present a successive convex-programming based sampling algorithm and establish its…
Sequential testing problems involve a complex system with several components, each of which is "working" with some independent probability. The outcome of each component can be determined by performing a test, which incurs some cost. The…
A powerful tool for studying long-term convergence of a Markov process to its stationary distribution is a Lyapunov function. In some sense, this is a substitute for eigenfunctions. For a stochastically ordered Markov process on the…
Herein, a methodology is developed to replicate functions, measures and stochastic processes onto a compact metric space. Many results are easily established for the replica objects and then transferred back to the original ones. Two…
In this paper, we consider the problem of approximating the spectral distribution for a class of random operators over sofic groups. For this purpose, we make use of the concept of locally and empirically converging measures defined by…
This paper compiles several aspects of the dynamics of stochastic approximation algorithms with Markov iterate-dependent noise when the iterates are not known to be stable beforehand. We achieve the same by extending the lock-in probability…
In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides…