Related papers: Stochastic Approximation and Modern Model-Based De…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…
Recently there has been increasing interest in alternate methods to compute quantum tunneling in field theory. Of particular interest is a stochastic approach which involves (i) sampling from the free theory Gaussian approximation to the…
This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…
We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…
Both for the theoretical and practical treatment of Inverse Problems, the modeling of the noise is a crucial part. One either models the measurement via a deterministic worst-case error assumption or assumes a certain stochastic behavior of…
System modeling is a classical approach to ensure their reliability since it is suitable both for a formal verification and for software testing techniques. In the context of model-based testing an approach combining random testing and…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
The quest for improved sampling methods to solve statistical mechanics problems of physical and chemical interest proceeds with renewed efforts since the invention of the Metropolis algorithm, in 1953. In particular, the understanding of…
Optimal design of a Phase I cancer trial can be formulated as a stochastic optimization problem. By making use of recent advances in approximate dynamic programming to tackle the problem, we develop an approximation of the Bayesian optimal…
Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…
Stochastic methods for minimizing a convex integral functional, as initiated by Robbins and Monro in the early 1950s, rely on the evaluation of a gradient (or subgradient if the function is not smooth) and moving in the corresponding…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
Benchmark dose analysis aims to estimate the level of exposure to a toxin that results in a clinically-significant adverse outcome and quantifies uncertainty using the lower limit of a confidence interval for this level. We develop a novel…
The Robbins-Siegmund theorem is one of the most important results in stochastic optimization, where it is widely used to prove the convergence of stochastic algorithms. We provide a quantitative version of the theorem, establishing a bound…
We study the Robbins-Monro stochastic approximation algorithm with projections on a hyperrectangle and prove its convergence. This work fills a gap in the convergence proof of the classic book by Kushner and Yin. Using the ODE method, we…
We study a diagnostic strategy which is based on the anticipation of the diagnostic process by simulation of the dynamical process starting from the initial findings. We show that such a strategy could result in more accurate diagnoses…
Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic…
An accurate estimation of the dose-response relationship is important to determine the optimal dose. For this purpose, a dose finding trial in which subjects are randomized to a few fixed dose levels is the most commonly used design. Often,…