Related papers: The acceptance-rejection method for low-discrepanc…
Monte Carlo dropout may effectively capture model uncertainty in deep learning, where a measure of uncertainty is obtained by using multiple instances of dropout at test time. However, Monte Carlo dropout is applied across the whole network…
Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically…
Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we…
Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…
Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…
In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted…
Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method…
Monte Carlo (MC) methods have become very popular in signal processing during the past decades. The adaptive rejection sampling (ARS) algorithms are well-known MC technique which draw efficiently independent samples from univariate target…
Quasi-Monte Carlo sampling can attain far better accuracy than plain Monte Carlo sampling. However, with plain Monte Carlo sampling it is much easier to estimate the attained accuracy. This article describes methods old and new to quantify…
ABC (approximate Bayesian computation) is a general approach for dealing with models with an intractable likelihood. In this work, we derive ABC algorithms based on QMC (quasi- Monte Carlo) sequences. We show that the resulting ABC…
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of…
This work introduces two new techniques for random number generation with any prescribed nonlinear distribution based on the k-vector methodology. The first approach is based on inverse transform sampling using the optimal k-vector to…
We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…
We present a method for Monte Carlo sampling on systems with discrete variables (focusing in the Ising case), introducing a prior on the candidate moves in a Metropolis-Hastings scheme which can significantly reduce the rejection rate,…
Equality-constrained models naturally arise in problems in which measurements are taken at different levels of resolution. The challenge in this setting is that the models usually induce a joint distribution which is intractable. Resorting…
The Metropolis-Hastings algorithm allows one to sample asymptotically from any probability distribution $\pi$. There has been recently much work devoted to the development of variants of the MH update which can handle scenarios where such…
In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…
We investigate the use of Antithetic Variables, Control Variates and Importance Sampling to reduce the statistical errors of option sensitivities calculated with the Likelihood Ratio Method in Monte Carlo. We show how Antithetic Variables…
We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to…
Diffusion processes with small noise conditioned to reach a target set are considered. The AMS algorithm is a Monte Carlo method that is used to sample such rare events by iteratively simulating clones of the process and selecting…