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Bayesian neural network models (BNN) have re-surged in recent years due to the advancement of scalable computations and its utility in solving complex prediction problems in a wide variety of applications. Despite the popularity and…
Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
Bayesian neural networks (BNNs) have received an increased interest in the last years. In BNNs, a complete posterior distribution of the unknown weight and bias parameters of the network is produced during the training stage. This…
Bayesian decision theory advocates the Bayes classifier as the optimal approach for minimizing the risk in machine learning problems. Current deep learning algorithms usually solve for the optimal classifier by \emph{implicitly} estimating…
Quantifying the uncertainty in the output of a neural network is essential for deployment in scientific or engineering applications where decisions must be made under limited or noisy data. Bayesian neural networks (BNNs) provide a…
Variational autoencoder (VAE) is a very successful generative model whose key element is the so called amortized inference network, which can perform test time inference using a single feed forward pass. Unfortunately, this comes at the…
In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the…
The parametrized post-Einsteinian (ppE) framework and its variants are widely used to probe gravity through gravitational-wave tests that apply to a large class of theories beyond general relativity. However, the ppE framework is not truly…
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…
The task of quantifying the inherent uncertainty associated with neural network predictions is a key challenge in artificial intelligence. Bayesian neural networks (BNNs) and deep ensembles are among the most prominent approaches to tackle…
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…
Simulation-based inference provides a powerful framework for Bayesian inference when the likelihood is analytically intractable or computationally prohibitive. By leveraging machine-learning techniques and neural density estimators, it…
Transfer learning has recently shown significant performance across various tasks involving deep neural networks. In these transfer learning scenarios, the prior distribution for downstream data becomes crucial in Bayesian model averaging…
Finding model parameters from data is an essential task in science and engineering, from weather and climate forecasts to plasma control. Previous works have employed neural networks to greatly accelerate finding solutions to inverse…
Gravitational waves emitted by a ringing black hole allow us to perform precision tests of general relativity in the strong field regime. With improvements to our current gravitational wave detectors and upcoming next-generation detectors,…
We revisit empirical Bayes in the absence of a tractable likelihood function, as is typical in scientific domains relying on computer simulations. We investigate how the empirical Bayesian can make use of neural density estimators first to…
Ensembles of independently trained neural networks are a state-of-the-art approach to estimate predictive uncertainty in Deep Learning, and can be interpreted as an approximation of the posterior distribution via a mixture of delta…
In recent years, neural networks have revolutionized various domains, yet challenges such as hyperparameter tuning and overfitting remain significant hurdles. Bayesian neural networks offer a framework to address these challenges by…
We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential…