Related papers: Parametric families on large binary spaces
We show that the variance of the Monte Carlo estimator that is importance sampled from an exponential family is a convex function of the natural parameter of the distribution. With this insight, we propose an adaptive importance sampling…
Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace and there is a large literature on MCMC theory and practice, MCMC users…
Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…
Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…
Adaptive sampling algorithms are modern and efficient methods that dynamically adjust the sample size throughout the optimization process. However, they may encounter difficulties in risk-averse settings, particularly due to the challenge…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article, we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables…
Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…
The Einstein field equations, or generalizations thereof, are difficult to solve analytically. On the other hand, numerical solutions of the same equations have become increasingly common, in particular concerning compact objects. Whereas…
Binary optimization has a wide range of applications in combinatorial optimization problems such as MaxCut, MIMO detection, and MaxSAT. However, these problems are typically NP-hard due to the binary constraints. We develop a novel…
Space filling designs are central to studying complex systems in various areas of science. They are used for obtaining an overall understanding of the behaviour of the response over the input space, model construction and uncertainty…
We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is "small" relative to the…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte…
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…