Related papers: Replacing Gaussian Processes with Neural Networks …
Bayesian nonparametric models, such as Gaussian processes, provide a compelling framework for automatic statistical modelling: these models have a high degree of flexibility, and automatically calibrated complexity. However, automating…
Bayesian neural networks utilize probabilistic layers that capture uncertainty over weights and activations, and are trained using Bayesian inference. Since these probabilistic layers are designed to be drop-in replacement of their…
We propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is…
Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without…
In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective. Although subsampling discards a large part of training data, we show provable guarantees…
A neural network (NN) is a parameterised function that can be tuned via gradient descent to approximate a labelled collection of data with high precision. A Gaussian process (GP), on the other hand, is a probabilistic model that defines a…
A large collection of time series poses significant challenges for classical and neural forecasting approaches. Classical time series models fail to fit data well and to scale to large problems, but succeed at providing uncertainty…
In this paper we cast the well-known convolutional neural network in a Gaussian process perspective. In this way we hope to gain additional insights into the performance of convolutional networks, in particular understand under what…
Long-term precise timing of Galactic millisecond pulsars holds great promise for measuring the long-period (months-to-years) astrophysical gravitational waves. Several gravitational-wave observational programs, called Pulsar Timing Arrays…
The incomplete sampling of data in complex polarization measurements from radio telescopes negatively affects both the rotation measure (RM) transfer function and the Faraday depth spectra derived from these data. Such gaps in polarization…
Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Mat\'ern kernel temporal Gaussian processes with respect to the kernel covariance function's hyperparameters. It is based…
The standard approaches to neural network implementation yield powerful function approximation capabilities but are limited in their abilities to learn meta representations and reason probabilistic uncertainties in their predictions.…
Learning the kernel parameters for Gaussian processes is often the computational bottleneck in applications such as online learning, Bayesian optimization, or active learning. Amortizing parameter inference over different datasets is a…
Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…
Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
In this paper we introduce a novel online time series forecasting model we refer to as the pM-GP filter. We show that our model is equivalent to Gaussian process regression, with the advantage that both online forecasting and online…
Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates,…
Structural kernels are a flexible learning paradigm that has been widely used in Natural Language Processing. However, the problem of model selection in kernel-based methods is usually overlooked. Previous approaches mostly rely on setting…
Numerical relativity (NR) enables the study of physics in strong and dynamical gravitational fields and provides predictions for the gravitational-wave signals produced by merging black holes. Despite the impressive accuracy of modern…