Related papers: Affine Tracing: A New Paradigm for Probabilistic L…

In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model…

In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…

Solving multiple parametrised related systems is an essential component of many numerical tasks, and learning from the already solved systems will make this process faster. In this work, we propose a novel probabilistic linear solver over…

The iterated posterior linearization filter (IPLF) is an algorithm for Bayesian state estimation that performs the measurement update using iterative statistical regression. The main result behind IPLF is that the posterior approximation is…

For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…

The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these…

This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately,…

Probabilistic models over strings have played a key role in developing methods allowing indels to be treated as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do…

In applications of Gaussian processes where quantification of uncertainty is of primary interest, it is necessary to accurately characterize the posterior distribution over covariance parameters. This paper proposes an adaptation of the…

In this paper, we develop a Bayesian multiscale approach based on a multiscale finite element method. Because of scale disparity in many multiscale applications, computational models can not resolve all scales. Various subgrid models are…

We introduce probabilistic language tries (PLTs), a unified representation that makes explicit the prefix structure implicitly defined by any generative model over sequences. By assigning to each outgoing edge the conditional probability of…

Spline basis exploration via Bayesian model selection is a widely employed strategy for determining the optimal set of basis terms in nonparametric regression. However, despite its widespread use, this approach often encounters performance…

Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on…

Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior…

Computing accurate periodic responses in strongly nonlinear or even non-smooth vibration systems remains a fundamental challenge in nonlinear dynamics. Existing numerical methods, such as the Harmonic Balance Method (HBM) and the Shooting…

Least-absolute-deviations (LAD) line fitting is robust to outliers but computationally more involved than least squares regression. Although the literature includes linear and near-linear time algorithms for the LAD line fitting problem,…

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving…

We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…

The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which…

Prior-data fitted networks (PFNs) have emerged as promising foundation models for prediction from tabular datasets, achieving state-of-the-art performance on small to moderate data sizes without tuning. While PFNs are motivated by Bayesian…