Related papers: Importance sampling-based gradient method for dime…
The shrinking rank method is a variation of slice sampling that is efficient at sampling from multivariate distributions with highly correlated parameters. It requires that the gradient of the log-density be computable. At each individual…
In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…
We propose an unconstrained stochastic approximation method of finding the optimal measure change (in an a priori parametric family) for Monte Carlo simulations. We consider different parametric families based on the Girsanov theorem and…
There has been considerable recent interest in Bayesian modeling of high-dimensional networks via latent space approaches. When the number of nodes increases, estimation based on Markov Chain Monte Carlo can be extremely slow and show poor…
We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed…
Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To…
In this paper we study probabilistic and neural network approximations for solutions to Poisson equation subject to Holder data in general bounded domains of $\mathbb{R}^d$. We aim at two fundamental goals. The first, and the most…
We study online inference and asymptotic covariance estimation for the stochastic gradient descent (SGD) algorithm. While classical methods (such as plug-in and batch-means estimators) are available, they either require inaccessible…
Zhang et al. introduced a novel modification of Goldstein's classical subgradient method, with an efficiency guarantee of $O(\varepsilon^{-4})$ for minimizing Lipschitz functions. Their work, however, makes use of a nonstandard subgradient…
Learning latent variable models with stochastic variational inference is challenging when the approximate posterior is far from the true posterior, due to high variance in the gradient estimates. We propose a novel rejection sampling step…
This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem…
Gradient descent is one of the most widely used iterative algorithms in modern statistical learning. However, its precise algorithmic dynamics in high-dimensional settings remain only partially understood, which has limited its broader…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or…
Bayesian inference for models with intractable likelihood functions represents a challenging suite of problems in modern statistics. In this work we analyse the Conway-Maxwell-Poisson (COM-Poisson) distribution, a two parameter…
Stochastic gradient methods are central to modern large-scale learning, but their use with incomplete covariates remains delicate since imputation schemes generally introduce systematic gradient biases, as shown for linear models. In this…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…
We derive methods to compute higher order differentials (Hessians and Hessian-vector products) of the rendering operator. Our approach is based on importance sampling of a convolution that represents the differentials of rendering…