Related papers: Source identification via pathwise gradient estima…

We combine conditional state density construction with an extension of the Scenario Approach for stochastic Model Predictive Control to nonlinear systems to yield a novel particle-based formulation of stochastic nonlinear output-feedback…

Distribution Regression (DR) on stochastic processes describes the learning task of regression on collections of time series. Path signatures, a technique prevalent in stochastic analysis, have been used to solve the DR problem. Recent…

Policy gradient methods are extensively used in reinforcement learning as a way to optimize expected return. In this paper, we explore the evolution of the policy parameters, for a special class of exactly solvable POMDPs, as a…

Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time…

Sampling from a high-dimensional distribution is a fundamental task in statistics, engineering, and the sciences. A canonical approach is the Langevin Algorithm, i.e., the Markov chain for the discretized Langevin Diffusion. This is the…

We first derive the Hamilton-Jacobi theory underlying continuous-time Markov processes, and then use the construction to develop a variational algorithm for estimating escape (least improbable or first passage) paths for a generic…

Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…

In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized…

We consider a change-point detection problem for a simple class of Piecewise Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in discrete time and through noise, and the aim is to propose a numerical method to…

The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, accurate determination of the underlying diffusive properties, beyond…

We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…

We consider stochastic optimization under distributional uncertainty, where the unknown distributional parameter is estimated from streaming data that arrive sequentially over time. Moreover, data may depend on the decision of the time when…

We study a variation of vanilla stochastic gradient descent where the optimizer only has access to a Markovian sampling scheme. These schemes encompass applications that range from decentralized optimization with a random walker (token…

We analyze the global and local behavior of gradient-like flows under stochastic errors towards the aim of solving convex optimization problems with noisy gradient input. We first study the unconstrained differentiable convex case, using a…

Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…

Multivariate data sources with components of different information value seem to appear frequently in practice. Models in which the components change their homogeneity at different times are of significant importance. The fact whether any…

Recent studies have demonstrated the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neural networks (PINNs). Source inversion problems under sparse…

This paper introduces Discrete Markov Probabilistic Models (DMPMs), a novel discrete diffusion algorithm for discrete data generation. The algorithm operates in discrete bit space, where the noising process is a continuous-time Markov chain…

We consider a distributed stochastic optimization problem in networks with finite number of nodes. Each node adjusts its action to optimize the global utility of the network, which is defined as the sum of local utilities of all nodes.…

We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…