Related papers: Optimal Monte Carlo Estimation of Belief Network I…
In this paper, we propose an efficient importance sampling algorithm for rare event simulation under copula models. In the algorithm, the derived optimal probability measure is based on the criterion of minimizing the variance of the…
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…
We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo (MCMC) method, with a fast mixing time and a much reduced susceptibility to…
Markov Chain Monte Carlo (MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. In this paper, we propose to approximate the log-likelihood…
Large language models (LLMs) have achieved significant performance gains via scaling up model sizes and/or data. However, recent evidence suggests diminishing returns from such approaches, motivating scaling the computation spent at…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This…
This paper discusses how two classes of approximate computation algorithms can be adapted, in a modular fashion, to achieve exact statistical inference from differentially private data products. Considered are approximate Bayesian…
Likelihood-free methods, such as approximate Bayesian computation, are powerful tools for practical inference problems with intractable likelihood functions. Markov chain Monte Carlo and sequential Monte Carlo variants of approximate…
Identifying future congestion points in electricity distribution networks is an important challenge distribution system operators face. A proven approach for addressing this challenge is to assess distribution grid adequacy using…
We propose a novel sampling framework for inference in probabilistic models: an active learning approach that converges more quickly (in wall-clock time) than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge in…
Multiple hypothesis tests are often carried out in practice using p-value estimates obtained with bootstrap or permutation tests since the analytical p-values underlying all hypotheses are usually unknown. This article considers the…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow.…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
In this note we propose a new approach towards solving numerically optimal stopping problems via reinforced regression based Monte Carlo algorithms. The main idea of the method is to reinforce standard linear regression algorithms in each…
This paper is on Bayesian inference for parametric statistical models that are defined by a stochastic simulator which specifies how data is generated. Exact sampling is then possible but evaluating the likelihood function is typically…
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…