Related papers: Active Probabilistic Inference on Matrices for Pre…

Machine learning practitioners invest significant manual and computational resources in finding suitable learning rates for optimization algorithms. We provide a probabilistic motivation, in terms of Gaussian inference, for popular…

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…

Leveraging machine learning methods to solve constraint satisfaction problems has shown promising, but they are mostly limited to a static situation where the problem description is completely known and fixed from the beginning. In this…

One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary…

We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A,…

The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…

Sketching techniques have become popular for scaling up machine learning algorithms by reducing the sample size or dimensionality of massive data sets, while still maintaining the statistical power of big data. In this paper, we study…

We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…

Perturbing a deterministic $n$-dimensional matrix with small Gaussian noise is a cornerstone of smoothed analysis of algorithms [Spielman and Teng, JACM 2004], as it reduces the condition number of the input to $O(n)$, and with it the…

Active inference has emerged as an alternative approach to control problems given its intuitive (probabilistic) formalism. However, despite its theoretical utility, computational implementations have largely been restricted to…

This paper develops a probabilistic anticipation algorithm for dynamic objects observed by an autonomous robot in an urban environment. Predictive Gaussian mixture models are used due to their ability to probabilistically capture continuous…

Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient-enhanced covariance matrix can be beneficial since it provides a more…

In engineering design, one often wishes to calculate the probability that the performance of a system is satisfactory under uncertainty. State of the art algorithms exist to solve this problem using active learning with Gaussian process…

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…

Purpose: Machine learning is broadly used for clinical data analysis. Before training a model, a machine learning algorithm must be selected. Also, the values of one or more model parameters termed hyper-parameters must be set. Selecting…

Many machine learning models require a training procedure based on running stochastic gradient descent. A key element for the efficiency of those algorithms is the choice of the learning rate schedule. While finding good learning rates…

We introduce a neural-preconditioned iterative solver for Poisson equations with mixed boundary conditions. Typical Poisson discretizations yield large, ill-conditioned linear systems. Iterative solvers can be effective for these problems,…

Recent advances in the field of machine learning open a new era in high performance computing. Applications of machine learning algorithms for the development of accurate and cost-efficient surrogates of complex problems have already…

This article introduces an iterative method for solving nonsingular non-Hermitian positive semidefinite systems of linear equations. To construct the iteration process, the coefficient matrix is split into two non-Hermitian positive…

We apply preconditioning, which is widely used in classical solvers for linear systems $A\textbf{x}=\textbf{b}$, to the variational quantum linear solver. By utilizing incomplete LU factorization as a preconditioner for linear equations…