Related papers: A Recursive Polynomial Chaos Evolution Method for …
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…
We introduce a novel stochastic version of the non-reversible, rejection-free Bouncy Particle Sampler (BPS), a Markov process whose sample trajectories are piecewise linear. The algorithm is based on simulating first arrival times in a…
We discuss a modification to Random Matrix Theory eigenstate statistics, that systematically takes into account the non-universal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead…
We explore the applicability of a stochastic time-evolution algorithm based on probabilistic angle interpolation. To simplify the pre-processing of the algorithm, we take the continuous-time limit, thereby explicitly eliminating Trotter…
The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…
This paper presents a solution for persistent monitoring of real-world stochastic phenomena, where the underlying covariance structure changes sharply across time, using a small number of mobile robot sensors. We propose an adaptive…
This work proposes a sampling-based (non-intrusive) approach within the context of low-rank separated representations to tackle the issue of curse-of-dimensionality associated with the solution of models, e.g., PDEs/ODEs, with…
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
The stochastic reaction network in which chemical species evolve through a set of reactions is widely used to model stochastic processes in physics, chemistry and biology. To characterize the evolving joint probability distribution in the…
Incorporating probabilistic terms in mathematical models is crucial for capturing and quantifying uncertainties in real-world systems, especially when the solution is not unique or exhibits sudden qualitative changes as parameters vary.…
Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…
The study presents a novel approach for stochastic nonlinear model updating in structural dynamics, employing a Bayesian framework integrated with Markov Chain Monte Carlo (MCMC) sampling for parameter estimation by using an approximated…
Motivated by techniques developed in recent progress on lower bounds for sublinear time algorithms (Behnezhad, Roghani and Rubinstein, STOC 2023, FOCS 2023, and STOC 2024) we introduce and study a new class of randomized algorithmic…
Recently, the use of Polynomial Chaos Expansion (PCE) has been increasing to study the uncertainty in mathematical models for a wide range of applications and several extensions of the original PCE technique have been developed to deal with…
This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we…
This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…
Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…
We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed…
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…
Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations…