Related papers: Monte Carlo Inference via Greedy Importance Sampli…

Monte Carlo algorithms, such as Markov chain Monte Carlo (MCMC) and Hamiltonian Monte Carlo (HMC), are routinely used for Bayesian inference in generalized linear models; however, these algorithms are prohibitively slow in massive data…

Understanding decisions made by neural networks is key for the deployment of intelligent systems in real world applications. However, the opaque decision making process of these systems is a disadvantage where interpretability is essential.…

We present a general sample reweighting scheme and its underlying theory for the integration of an unknown function with low dimensionality. Our method produces better results than standard weighting schemes for common sampling strategies,…

The sampling importance resampling method is widely utilized in various fields, such as numerical integration and statistical simulation. In this paper, two modified methods are presented by incorporating two variance reduction techniques…

Many generative models can be expressed as a differentiable function of random inputs drawn from some simple probability density. This framework includes both deep generative architectures such as Variational Autoencoders and a large class…

Improving efficiency of importance sampler is at the center of research in Monte Carlo methods. While adaptive approach is usually difficult within the Markov Chain Monte Carlo framework, the counterpart in importance sampling can be…

Kernel methods have revolutionized the fields of pattern recognition and machine learning. Their success, however, critically depends on the choice of kernel parameters. Using Gaussian process (GP) classification as a working example, this…

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…

Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…

Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…

Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…

In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…

Recent advances in machine learning have led to the development of new methods for enhancing Monte Carlo methods such as Markov chain Monte Carlo (MCMC) and importance sampling (IS). One such method is normalizing flows, which use a neural…

Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) algorithm for estimating expectations with respect to continuous un-normalized probability distributions. MCMC estimators typically have higher variance than…

Discrepancies play an important role in the study of uniformity properties of point sets. Their probability distributions are a help in the analysis of the efficiency of the Quasi Monte Carlo method of numerical integration, which uses…

Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance,…

We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…

One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…

Bayesian reasoning in linear mixed-effects models (LMMs) is challenging and often requires advanced sampling techniques like Markov chain Monte Carlo (MCMC). A common approach is to write the model in a probabilistic programming language…