Related papers: A Linear Programming Approach to Error Bounds for …

Regularized Markov Decision Processes serve as models of sequential decision making under uncertainty wherein the decision maker has limited information processing capacity and/or aversion to model ambiguity. With functional approximation,…

We take the point of view of a particle performing random walk with bounded jumps on $\mathbb{Z}^d$ in a stationary and ergodic random environment. We prove the quenched large deviation principle (LDP) for the pair empirical measure of the…

Quantum walks behave differently from what we expect and their probability distributions have unique structures. They have localization, singularities, a gap, and so on. Those features have been discovered from the view point of mathematics…

We consider a multivariate piecewise linear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured by the integrated mean square error. Multivariate piecewise linear interpolator is…

We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity…

Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…

Let $X$ be the constrained random walk on $\mathbb{Z}_+^d$ $d >2$, having increments $e_1$, $-e_i+e_{i+1}$ $i=1,2,3,...,d-1$ and $-e_d$ with probabilities $\lambda$, $\mu_1$, $\mu_2$,...,$\mu_d$, where $\{e_1,e_2,..,e_d\}$ are the standard…

The Random Walks (RW) algorithm is one of the most e - cient and easy-to-use probabilistic segmentation methods. By combining contrast terms with prior terms, it provides accurate segmentations of medical images in a fully automated manner.…

We tackle some fundamental problems in probability theory on corrupted random processes on the integer line. We analyze when a biased random walk is expected to reach its bottommost point and when intervals of integer points can be detected…

We present an analytical approach to study simple symmetric random walks (RWs) on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the…

An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…

The number of steps until termination of a probabilistic program is a random variable. Probabilistic program termination therefore requires qualitative analysis via almost-sure termination (AST), while also providing quantitative answers…

This paper gives various asymptotic formulae for the transition probability associated with discrete time quantum walks on the real line. The formulae depend heavily on the `normalized' position of the walk. When the position is in the…

When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…

The random walk Metropolis (RWM) is one of the most common Markov chain Monte Carlo algorithms in practical use today. Its theoretical properties have been extensively explored for certain classes of target, and a number of results with…

Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…

We study both the value function and Q-function formulation of the Linear Programming approach to Approximate Dynamic Programming. The approach is model-based and optimizes over a restricted function space to approximate the value function…

Linear fractional Galton-Watson branching processes in i.i.d.~random environment are, on the quenched level, intimately connected to random difference equations by the evolution of the random parameters of their linear fractional marginals.…

For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems (MBPs) with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front,…