相关论文: Frank-Wolfe Bayesian Quadrature: Probabilistic Int…

In this paper, we consider Frank-Wolfe-based algorithms for composite convex optimization problems with objective involving a logarithmically-homogeneous, self-concordant functions. Recent Frank-Wolfe-based methods for this class of…

Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Symmetric nonnegative matrix factorization has found abundant applications in various domains by providing a symmetric low-rank decomposition of nonnegative matrices. In this paper we propose a Frank-Wolfe (FW) solver to optimize the…

Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex…

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…

The Frank-Wolfe (FW) method is a popular algorithm for solving large-scale convex optimization problems appearing in structured statistical learning. However, the traditional Frank-Wolfe method can only be applied when the feasible region…

The stochastic Frank-Wolfe method has recently attracted much general interest in the context of optimization for statistical and machine learning due to its ability to work with a more general feasible region. However, there has been a…

The Frank Wolfe algorithm (FW) is a popular projection-free alternative for solving large-scale constrained optimization problems. However, the FW algorithm suffers from a sublinear convergence rate when minimizing a smooth convex function…

The automation of posterior inference in Bayesian data analysis has enabled experts and nonexperts alike to use more sophisticated models, engage in faster exploratory modeling and analysis, and ensure experimental reproducibility. However,…

Monte Carlo integration is a widely used numerical method for approximating integrals, which is often computationally expensive. In recent years, quantum computing has shown promise for speeding up Monte Carlo integration, and several…

We study Frank-Wolfe (FW) methods for constrained bilevel optimization when the lower-level problem is solved only approximately, yielding biased and inexact hypergradients. We analyze inexact variants of vanilla FW as well as away-step and…

We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian…

In applied Bayesian inference scenarios, users may have access to a large number of pre-existing model evaluations, for example from maximum-a-posteriori (MAP) optimization runs. However, traditional approximate inference techniques make…

We explore computational aspects of maximum likelihood estimation of the mixture proportions of a nonparametric finite mixture model -- a convex optimization problem with old roots in statistics and a key member of the modern data analysis…

Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…

This paper contributes to the study of optimal experimental design for Bayesian inverse problems governed by partial differential equations (PDEs). We derive estimates for the parametric regularity of multivariate double integration…

Bayesian quadrature (BQ) is a sample-efficient probabilistic numerical method to solve integrals of expensive-to-evaluate black-box functions, yet so far,active BQ learning schemes focus merely on the integrand itself as information source,…

We present an improved Bayesian framework for performing inference of affine transformations of constrained functions. We focus on quadrature with nonnegative functions, a common task in Bayesian inference. We consider constraints on the…