Related papers: BI-EqNO: Generalized Approximate Bayesian Inferenc…

Seemingly unrelated regression is a natural framework for regressing multiple correlated responses on multiple predictors. The model is very flexible, with multiple linear regression and covariance selection models being special cases.…

Bayesian Neural Networks (BNNs) place priors over the parameters in a neural network. Inference in BNNs, however, is difficult; all inference methods for BNNs are approximate. In this work, we empirically compare the quality of predictive…

We present a theory-first framework that interprets inference-time adaptation in large language models (LLMs) as online Bayesian state estimation. Rather than modeling rapid adaptation as implicit optimization or meta-learning, we formulate…

As a compact representation of joint probability distributions over a dependence graph of random variables, and a tool for modelling and reasoning in the presence of uncertainty, Bayesian networks are of great importance for artificial…

Despite their theoretical appealingness, Bayesian neural networks (BNNs) are left behind in real-world adoption, mainly due to persistent concerns on their scalability, accessibility, and reliability. In this work, we develop the…

In many real-world problems, there is a limited set of training data, but an abundance of unlabeled data. We propose a new method, Generative Posterior Networks (GPNs), that uses unlabeled data to estimate epistemic uncertainty in…

We formulate Ensemble-Conditional Gaussian Processes (Ens-CGP), a finite-dimensional synthesis that centers ensemble-based inference on the conditional Gaussian law. Conditional Gaussian processes (CGP) arise directly from Gaussian…

Bayesian neural networks (BNNs) provide a formalism to quantify and calibrate uncertainty in deep learning. Current inference approaches for BNNs often resort to few-sample estimation for scalability, which can harm predictive performance,…

Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI…

Bayesian inference affords scientists with powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of…

Bayesian learning is ubiquitous for implementing classification and regression tasks, however, it is accompanied by computationally intractable limitations when the feature spaces become extremely large. Aiming to solve this problem, we…

While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational…

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,…

Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component…

Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs…

Neural operators improve conventional neural networks by expanding their capabilities of functional mappings between different function spaces to solve partial differential equations (PDEs). One of the most notable methods is the Fourier…

In likelihood-free settings where likelihood evaluations are intractable, approximate Bayesian computation (ABC) addresses the formidable inference task to discover plausible parameters of simulation programs that explain the observations.…

Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…

We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…

Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and…