Related papers: Data-Driven Approximations of Chance Constrained P…
We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the…
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…
Stochastic variance reduced methods have shown strong performance in solving finite-sum problems. However, these methods usually require the users to manually tune the step-size, which is time-consuming or even infeasible for some…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
In power system operation, characterizing the stochastic nature of wind power is an important albeit challenging issue. It is well known that distributions of wind power forecast errors often exhibit significant variability with respect to…
Discrete time analogues of ergodic stochastic differential equations (SDEs) are one of the most popular and flexible tools for sampling high-dimensional probability measures. Non-asymptotic analysis in the $L^2$ Wasserstein distance of…
Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address…
Domain adaptation (DA) is an important and emerging field of machine learning that tackles the problem occurring when the distributions of training (source domain) and test (target domain) data are similar but different. Current theoretical…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
Posterior contractions rates (PCRs) strengthen the notion of Bayesian consistency, quantifying the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of the true model, with probability tending to 1 or…
Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference…
Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space…
Chance-constrained problems involve stochastic components in the constraints which can be violated with a small probability. We investigate the impact of different types of chance constraints on the performance of iterative search…
Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…
Stochastic and conditional simulation methods have been effective towards producing realistic realizations and simulations of spatial numerical models that share equal probability of occurrence. Application of these methods are valuable…
The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…
The likelihood-free sequential Approximate Bayesian Computation (ABC) algorithms, are increasingly popular inference tools for complex biological models. Such algorithms proceed by constructing a succession of probability distributions over…
We propose a new functional analytic approach to Stein's method of exchangeable pairs that does not require the pair at hand to satisfy any approximate linear regression property. We make use of this theory in order to derive abstract…
This paper considers a distributed stochastic optimization problem where the goal is to minimize the time average of a cost function subject to a set of constraints on the time averages of a related stochastic processes called penalties. We…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…