相关论文: Individual confidence intervals for true solutions…
Stochastic natural gradient variational inference (NGVI) is a popular and efficient algorithm for Bayesian inference. Despite empirical success, the convergence of this method is still not fully understood. In this work, we define and study…
Uncertainty quantification, by means of confidence interval (CI) construction, has been a fundamental problem in statistics and also important in risk-aware decision-making. In this paper, we revisit the basic problem of CI construction,…
Corrected confidence intervals are developed for the mean of the second component of a bivariate normal process when the first component is being monitored sequentially. This is accomplished by constructing a first approximation to a…
In this paper, we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems, and variational inequalities. This framework allows obtaining many…
One key challenge for solving a general stochastic optimization problem with expectations in the objective and constraint functions using ordinary stochastic iterative methods lies in the infeasibility issue caused by the randomness over…
We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds…
Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a…
We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and…
A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale.…
The Sequential Fully Implicit (SFI) method was proposed to simulate coupled immiscible multiphase fluid flow in porous media. Later, it was extended to the black-oil model, whereby the gas component is allowed to dissolve in the oil phase.…
Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…
This paper presents three new computational methods for calculating design sensitivities of statistical moments and reliability of high-dimensional complex systems subject to random input. The first method represents a novel integration of…
Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification. We propose predictive variational inference…
Profile likelihood confidence intervals are a robust alternative to Wald's method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood…
The Solvency Capital Requirement (SCR) calculation is computationally intensive, relying on the market-consistent estimation of own funds. While Solvency II prioritizes the direct valuation method, it theoretically yields the same value as…
We analyze algorithms for solving stochastic variational inequalities (VI) without the bounded variance or bounded domain assumptions, where our main focus is min-max optimization with possibly unbounded constraint sets. We focus on two…
In this paper, we propose several novel numerical techniques to deal with nonlinear terms in gradient flows. These step-by-step solving schemes, termed 3S-SAV and 3S-IEQ schemes, are based on recently popular scalar auxiliary variable (SAV)…
Statistical models are central to machine learning with broad applicability across a range of downstream tasks. The models are controlled by free parameters that are typically estimated from data by maximum-likelihood estimation or…
Owing to the recent advances in "Big Data" modeling and prediction tasks, variational Bayesian estimation has gained popularity due to their ability to provide exact solutions to approximate posteriors. One key technique for approximate…
In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…