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Bayesian Inference offers principled tools to tackle many critical problems with modern neural networks such as poor calibration and generalization, and data inefficiency. However, scaling Bayesian inference to large architectures is…

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…

Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…

Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on…

Latent Gaussian models (LGMs) are a popular class of Bayesian hierarchical models that include Gaussian processes, as well as certain spatial models and mixed-effect models. Efficient Bayesian inference of LGMs often requires marginalizing…

A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…

The ubiquitous backpropagation algorithm requires sequential updates through the network introducing a locking problem. In addition, back-propagation relies on the transpose of forward weight matrices to compute updates, introducing a…

We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on…

rdering of regression or classification coefficients occurs in many real-world applications. Fused Lasso exploits this ordering by explicitly regularizing the differences between neighboring coefficients through an $\ell_1$ norm…

We introduce a new framework called linear algebraic number theory (LANT) that reformulates the number-theoretic problem as a regression model and solves it using matrix algebra. This framework restricts all computations to log space,…

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…

We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior…

This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the…

Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…

While Large Language Models (LLMs) exhibit exceptional zero-shot relevance modeling, their high computational cost necessitates framing passage retrieval as a budget-constrained global optimization problem. Existing approaches passively…

Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used…

In the paper, we present a strategy for accelerating posterior inference for unknown inputs in time fractional diffusion models. In many inference problems, the posterior may be concentrated in a small portion of the entire prior support.…

Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the…

Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…

The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…