Related papers: Towards Expressive Priors for Bayesian Neural Netw…

Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…

Encoding domain knowledge into the prior over the high-dimensional weight space of a neural network is challenging but essential in applications with limited data and weak signals. Two types of domain knowledge are commonly available in…

Reference priors are theoretically attractive for the analysis of geostatistical data since they enable automatic Bayesian analysis and have desirable Bayesian and frequentist properties. But their use is hindered by computational hurdles…

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…

We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models while maintaining a distribution over weight-space with full support. Other scalable Bayesian deep learning…

Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of…

Autoregressive and recurrent networks have achieved remarkable progress across various fields, from weather forecasting to molecular generation and Large Language Models. Despite their strong predictive capabilities, these models lack a…

Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…

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…

Bayesian Neural Networks (BNNs) have recently received increasing attention for their ability to provide well-calibrated posterior uncertainties. However, model selection---even choosing the number of nodes---remains an open question. In…

Progress in neuroscience has provided unprecedented opportunities to advance our understanding of brain alterations and their correspondence to phenotypic profiles. With data collected from various imaging techniques, studies have…

This paper introduces a new neural network based prior for real valued functions on $\mathbb R^d$ which, by construction, is more easily and cheaply scaled up in the domain dimension $d$ compared to the usual Karhunen-Lo\`eve function space…

Neural networks capable of accurate, input-conditional uncertainty representation are essential for real-world AI systems. Deep ensembles of Gaussian networks have proven highly effective for continuous regression due to their ability to…

This paper introduces a periodic multivariate Poisson autoregression with potentially infinite memory, with a special focus on the network setting. Using contraction techniques, we study the stability of such a process and provide upper…

Feed-forward neural networks can be understood as a combination of an intermediate representation and a linear hypothesis. While most previous works aim to diversify the representations, we explore the complementary direction by performing…

Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few…

Neural networks are powerful tools for cognitive modeling due to their flexibility and emergent properties. However, interpreting their learned representations remains challenging due to their sub-symbolic semantics. In this work, we…

To adopt neural networks in safety critical domains, knowing whether we can trust their predictions is crucial. Bayesian neural networks (BNNs) provide uncertainty estimates by averaging predictions with respect to the posterior weight…

Gaussian processes are ubiquitous in nature and engineering. A case in point is a class of neural networks in the infinite-width limit, whose priors correspond to Gaussian processes. Here we perturbatively extend this correspondence to…

This work studies nonparametric Bayesian estimation of the intensity function of an inhomogeneous Poisson point process in the important case where the intensity depends on covariates, based on the observation of a single realisation of the…