相关论文: RPEM: Randomized Monte Carlo Parametric Expectatio…

We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…

Stochastic Differential Equations (SDEs) are used as statistical models in many disciplines. However, intractable likelihood functions for SDEs make inference challenging, and we need to resort to simulation-based techniques to estimate and…

We investigate in this paper an alternative method to simulation based recursive importance sampling procedure to estimate the optimal change of measure for Monte Carlo simulations. We propose an algorithm which combines (vector and…

Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on…

The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…

Bayesian inference for hierarchical models can be very challenging. MCMC methods have difficulty scaling to large models with many observations and latent variables. While variational inference (VI) and reweighted wake-sleep (RWS) can be…

This paper proposes a synergy of amortised and particle-based methods for sampling from distributions defined by unnormalised density functions. We state a connection between sequential Monte Carlo (SMC) and neural sequential samplers…

The Markov chain Monte Carlo method (MCMC), especially the Metropolis-Hastings (MH) algorithm, is a widely used technique for sampling from a target probability distribution $P$ on a state space $\Omega$ and applied to various problems such…

In this paper, we present an online reinforcement learning algorithm, called Renewal Monte Carlo (RMC), for infinite horizon Markov decision processes with a designated start state. RMC is a Monte Carlo algorithm and retains the advantages…

We propose a Multi-level Monte Carlo technique to accelerate Monte Carlo sampling for approximation of properties of materials with random defects. The computational efficiency is investigated on test problems given by tight-binding models…

Deep learning algorithms have been widely used to solve linear Kolmogorov partial differential equations~(PDEs) in high dimensions, where the loss function is defined as a mathematical expectation. We propose to use the randomized…

We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and…

Monte Carlo methods are widely used to estimate observables in many-body quantum systems. However, conventional sampling schemes often require a large number of samples to achieve sufficient accuracy. In this work we propose the…

This paper provides a framework in which multilevel Monte Carlo and continuous level Monte Carlo can be compared. In continuous level Monte Carlo the level of refinement is determined by an exponentially distributed random variable, which…

We introduce Projected Latent Markov Chain Monte Carlo (PL-MCMC), a technique for sampling from the high-dimensional conditional distributions learned by a normalizing flow. We prove that a Metropolis-Hastings implementation of PL-MCMC…

Stochastic PDE eigenvalue problems often arise in the field of uncertainty quantification, whereby one seeks to quantify the uncertainty in an eigenvalue, or its eigenfunction. In this paper we present an efficient multilevel quasi-Monte…

The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much…

With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…

Finite mixture models are powerful tools for modelling and analyzing heterogeneous data. Parameter estimation is typically carried out using maximum likelihood estimation via the Expectation-Maximization (EM) algorithm. Recently, the…

We introduce a modification of the well-known Metropolis importance sampling algorithm by using a methodology inspired on the consideration of the reparametrization invariance of the microcanonical ensemble. The most important feature of…