Related papers: Stochastic variance-reduced Gaussian variational i…

Variational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence. A…

Given a multivariate function taking deterministic and uncertain inputs, we consider the problem of estimating a quantile set: a set of deterministic inputs for which the probability that the output belongs to a specific region remains…

We develop a pure Monte Carlo method to compute $E(g(X_T))$ where $g$ is a bounded and Lipschitz function and $X_t$ an Ito process. This approach extends a previously proposed method to the general multidimensional case with a SDE with…

This paper studies the use of a machine learning-based estimator as a control variate for mitigating the variance of Monte Carlo sampling. Specifically, we seek to uncover the key factors that influence the efficiency of control variates in…

Variational inference (VI) can be cast as an optimization problem in which the variational parameters are tuned to closely align a variational distribution with the true posterior. The optimization task can be approached through vanilla…

Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL)…

Variational wave functions used in the variational Monte Carlo (VMC) method are extensively improved to overcome the biases coming from the assumed variational form of the wave functions. We construct a highly generalized variational form…

For a class of stochastic models with Gaussian and rough mean-reverting volatility that embeds the genuine rough Stein-Stein model, we study the weak approximation rate when using a Euler type scheme with integrated kernels. Our first…

Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…

We present a novel approach to approximate Gaussian and mixture-of-Gaussians filtering. Our method relies on a variational approximation via a gradient-flow representation. The gradient flow is derived from a Kullback--Leibler discrepancy…

Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…

We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow.…

Bayesian model comparison relies upon the model evidence, yet for many models of interest the model evidence is unavailable in closed form and must be approximated. Many of the estimators for evidence that have been proposed in the Monte…

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

Robustness to outliers is a central issue in real-world machine learning applications. While replacing a model to a heavy-tailed one (e.g., from Gaussian to Student-t) is a standard approach for robustification, it can only be applied to…

We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations,…

A method for selecting a graphical model for $p$-vector-valued stationary Gaussian time series was recently proposed by Matsuda and uses the Kullback-Leibler divergence measure to define a test statistic. This statistic was used in a…

Variational logistic regression is a popular method for approximate Bayesian inference seeing wide-spread use in many areas of machine learning including: Bayesian optimization, reinforcement learning and multi-instance learning to name a…

We propose a variational method to solve all three estimation problems for nonlinear stochastic dynamical systems: prediction, filtering, and smoothing. Our new approach is based upon a proper choice of cost function, termed the {\it…

Bayesian parameter inference for complex stochastic simulators is challenging due to intractable likelihood functions. Existing simulation-based inference methods often require large number of simulations and become costly to use in…