Related papers: Replacing Gaussian Processes with Neural Networks …

Finding and characterizing gravitational waves from individual supermassive black hole binaries is a central goal of pulsar timing array experiments, which will require analysis methods that can be efficient on our rapidly growing datasets.…

We explore the link between deep ensembles and Gaussian processes (GPs) through the lens of the Neural Tangent Kernel (NTK): a recent development in understanding the training dynamics of wide neural networks (NNs). Previous work has shown…

In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…

Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…

Studies have shown that the use of pulsar timing arrays (PTAs) is among the approaches with the highest potential to detect very low-frequency gravitational waves in the near future. Although the capture of gravitational waves (GWs) by PTAs…

Graph Neural Networks (GNNs) have advanced spatiotemporal forecasting by leveraging relational inductive biases among sensors (or any other measuring scheme) represented as nodes in a graph. However, current methods often rely on Recurrent…

Modern simulation-based inference techniques use neural networks to solve inverse problems efficiently. One notable strategy is neural posterior estimation (NPE), wherein a neural network parameterizes a distribution to approximate the…

Neal (1996) proved that infinitely wide shallow Bayesian neural networks (BNN) converge to Gaussian processes (GP), when the network weights have bounded prior variance. Cho & Saul (2009) provided a useful recursive formula for deep kernel…

Neural network pruning is a highly effective technique aimed at reducing the computational and memory demands of large neural networks. In this research paper, we present a novel approach to pruning neural networks utilizing Bayesian…

Automatic forecasting is the task of receiving a time series and returning a forecast for the next time steps without any human intervention. Gaussian Processes (GPs) are a powerful tool for modeling time series, but so far there are no…

Pulsar Timing Array (PTA) collaborations recently reported evidence for the presence of a gravitational wave background (GWB) in their datasets. The main candidate that is expected to produce such a GWB is the population of supermassive…

Bayesian neural networks provide a direct and natural way to extend standard deep neural networks to support probabilistic deep learning through the use of probabilistic layers that, traditionally, encode weight (and bias) uncertainty. In…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

This paper presents a probabilistic framework to obtain both reliable and fast uncertainty estimates for predictions with Deep Neural Networks (DNNs). Our main contribution is a practical and principled combination of DNNs with sparse…

Pulsar timing array experiments have recently reported strong evidence for a common-spectrum stochastic process with a strain spectral index consistent with that expected of a nanohertz-frequency gravitational-wave background, but with…

In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…

The recent detection of nanohertz stochastic gravitational-wave backgrounds (SGWBs) by pulsar timing arrays (PTAs) promises unique insights into astrophysical and cosmological origins. However, traditional Markov Chain Monte Carlo (MCMC)…

Artificial neural networks (NNs) are one of the most frequently used machine learning approaches to construct interatomic potentials and enable efficient large-scale atomistic simulations with almost ab initio accuracy. However, the…

We describe an analysis of the First International Pulsar Timing Array Data Challenge. We employ a robust, unbiased Bayesian framework developed by van Haasteren to study the three Open and Closed datasets, testing various models for each…

Capsule Networks attempt to represent patterns in images in a way that preserves hierarchical spatial relationships. Additionally, research has demonstrated that these techniques may be robust against adversarial perturbations. We present…