Related papers: Accelerated Parameter Estimation with DALE$\chi$

In this work, we study the approximation of expected values of functional quantities on the solution of a stochastic differential equation (SDE), where we replace the Monte Carlo estimation with the evaluation of a deep neural network. Once…

Markov Chain Monte Carlo (MCMC) methods are employed to sample from a given distribution of interest, whenever either the distribution does not exist in closed form, or, if it does, no efficient method to simulate an independent sample from…

This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the…

State-space models have been used in many applications, including econometrics, engineering, medical research, etc. The maximum likelihood estimation (MLE) of the static parameter of general state-space models is not straightforward because…

Markov Chain Monte Carlo (MCMC) sampling is computationally expensive, especially for complex models. Alternative methods make simplifying assumptions about the posterior to reduce computational burden, but their impact on predictive…

This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…

While Monte Carlo Tree Search (MCTS) shows promise in Large Language Model (LLM) based Automatic Heuristic Design (AHD), it suffers from a critical over-exploitation tendency under the limited computational budgets required for heuristic…

Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…

We propose and analyze algorithms for distributionally robust optimization of convex losses with conditional value at risk (CVaR) and $\chi^2$ divergence uncertainty sets. We prove that our algorithms require a number of gradient…

Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We…

We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast, iterative approximations to the target density to speculatively evaluate many potential…

Recently, it has been proposed in the literature to employ deep neural networks (DNNs) together with stochastic gradient descent methods to approximate solutions of PDEs. There are also a few results in the literature which prove that DNNs…

Quantifying the uncertainty in model parameters and output is a critical component in model-driven decision support systems for groundwater management. This paper presents a novel algorithmic approach which fuses Markov Chain Monte Carlo…

We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization…

This survey article is concerned with the application of lattice rules to Deep Neural Networks (DNNs), lattice rules being a family of quasi-Monte Carlo methods. They have demonstrated effectiveness in various contexts for high-dimensional…

Monte Carlo simulations of quantum field theories on a lattice become increasingly expensive as the continuum limit is approached since the cost per independent sample grows with a high power of the inverse lattice spacing. Simulations on…

Maximum likelihood estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution that best explain the observed data. In the context of text generation, MLE is often used to train generative language…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Markov chain Monte Carlo (MCMC) provides asymptotically consistent estimates of intractable posterior expectations as the number of iterations tends to infinity. However, in large data applications, MCMC can be computationally expensive per…

We present Automatic Laplace Collapsed Sampling (ALCS), a general framework for marginalising latent parameters in Bayesian models using automatic differentiation, which we combine with nested sampling to explore the hyperparameter space in…