Related papers: Rao-Blackwellization in the MCMC era

We introduce overdispersed black-box variational inference, a method to reduce the variance of the Monte Carlo estimator of the gradient in black-box variational inference. Instead of taking samples from the variational distribution, we use…

The Monte Carlo (MC) method is the most common technique used for uncertainty quantification, due to its simplicity and good statistical results. However, its computational cost is extremely high, and, in many cases, prohibitive.…

We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly…

We consider Metropolis Hastings MCMC in cases where the log of the ratio of target distributions is replaced by an estimator. The estimator is based on m samples from an independent online Monte Carlo simulation. Under some conditions on…

As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…

In this report, we present qualitative analysis of Monte Carlo (MC) dropout method for measuring model uncertainty in neural network (NN) models. We first consider the sources of uncertainty in NNs, and briefly review Bayesian Neural…

In this paper a method based on a Markov chain Monte Carlo (MCMC) algorithm is proposed to compute the probability of a rare event. The conditional distribution of the underlying process given that the rare event occurs has the probability…

Monte Carlo significance tests are a general tool that produce p-values by generating samples from the null distribution. However, Monte Carlo tests are limited to null hypothesis which we can exactly sample from. Markov chain Monte Carlo…

We provide the first convergence guarantee for full black-box variational inference (BBVI), also known as Monte Carlo variational inference. While preliminary investigations worked on simplified versions of BBVI (e.g., bounded domain,…

A simple criterion is presented for a practical construction of generalized moments that allow one to approach the theoretical Rao-Cramer limit for parameter estimation while avoiding the complexity of the maximum likelihood method in the…

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…

Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…

Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where…

Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…

Counterfactual explanations are one of the most popular methods to make predictions of black box machine learning models interpretable by providing explanations in the form of `what-if scenarios'. Most current approaches optimize a…

Predictive models in ML need to be trustworthy and reliable, which often at the very least means outputting calibrated probabilities. This can be particularly difficult to guarantee in the online prediction setting when the outcome sequence…

In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same…

An introduction to the basics of Monte Carlo is given. The topics covered include, sample space, events, probabilities, random variables, mean, variance, covariance, characteristic function, chebyshev inequality, law of large numbers,…

In this paper, we examine the CE method in the broad context of Monte Carlo Optimization (MCO) and Parametric Learning (PL), a type of machine learning. A well-known overarching principle used to improve the performance of many PL…

A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…