相关论文: Statistical Properties of the Probabilistic Numeri…

In this article, we study the binary classification problem with supervised data, in the case where the covariate-to-probability-of-success map is possibly spatially inhomogeneous. We devise nonparametric Bayesian procedures with…

Approximate Bayesian Computation (ABC) enables statistical inference in simulator-based models whose likelihoods are difficult to calculate but easy to simulate from. ABC constructs a kernel-type approximation to the posterior distribution…

In this work, solvers and preconditioners based on Gauss-Seidel and Jacobi algorithms are explored for stochastic Galerkin discretization of partial differential equations (PDEs) with random input data. Gauss-Seidel and Jacobi algorithms…

Enlarged Krylov subspace methods and their s-step versions were introduced [7] in the aim of reducing communication when solving systems of linear equations Ax = b. These enlarged CG methods consist of enlarging the Krylov subspace by a…

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…

Accurate uncertainty quantification is critical for reliable predictive modeling. Existing methods typically address either aleatoric uncertainty due to measurement noise or epistemic uncertainty resulting from limited data, but not both in…

The conjugate gradient (CG) method is a classic Krylov subspace method for solving symmetric positive definite linear systems. We introduce an analogous semi-conjugate gradient (SCG) method for unsymmetric positive definite linear systems.…

Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…

For many applications of probabilistic classifiers it is important that the predicted confidence vectors reflect true probabilities (one says that the classifier is calibrated). It has been shown that common models fail to satisfy this…

The problem of optimal precision switching for the conjugate gradient (CG) method applied to sparse linear systems is considered. A sparse matrix is defined as an $n\!\times\!n$ matrix with $m\!=\!O(n)$ nonzero entries. The algorithm first…

The Complex Langevin (CL) method to simulate `complex probabilities', ideally produces expectation values for the observables that converge to a limit equal to the expectation values obtained with the original complex `probability' measure.…

Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks.…

A suitable scalar metric can help measure multi-calibration, defined as follows. When the expected values of observed responses are equal to corresponding predicted probabilities, the probabilistic predictions are known as "perfectly…

Recently, enlarged Krylov subspace methods, that consists of enlarging the Krylov subspace by a maximum of t vectors per iteration based on the domain decomposition of the graph of A, were introduced in the aim of reducing communication…

We study the fundamental problem of calibrating a linear binary classifier of the form $\sigma(\hat{w}^\top x)$, where the feature vector $x$ is Gaussian, $\sigma$ is a link function, and $\hat{w}$ is an estimator of the true linear weight…

Krylov subspace methods are widely known as efficient algebraic methods for solving large scale linear systems. However, on massively parallel hardware the performance of these methods is typically limited by communication latency rather…

By reducing the number of global synchronization bottlenecks per iteration and hiding communication behind useful computational work, pipelined Krylov subspace methods achieve significantly improved parallel scalability on present-day HPC…

This paper establishes the asymptotic consistency of the {\it loss-calibrated variational Bayes} (LCVB) method. LCVB was proposed in~\cite{LaSiGh2011} as a method for approximately computing Bayesian posteriors in a `loss aware' manner.…

Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often…

For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by Gaussian white noise, the Lanczos bidiagonalization based Krylov solver LSQR and its mathematically equivalent CGLS, the Conjugate…