Related papers: The Gaussian Neural Process
We introduce Markov Neural Processes (MNPs), a new class of Stochastic Processes (SPs) which are constructed by stacking sequences of neural parameterised Markov transition operators in function space. We prove that these Markov transition…
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…
Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…
Gaussian process training decomposes into inference of the (approximate) posterior and learning of the hyperparameters. For non-Gaussian (non-conjugate) likelihoods, two common choices for approximate inference are Expectation Propagation…
The ability to deal with uncertainty in machine learning models has become equally, if not more, crucial to their predictive ability itself. For instance, during the pandemic, governmental policies and personal decisions are constantly made…
Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about…
In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational bottleneck with exact GP modeling, we employ…
Systems based on artificial neural networks (ANNs) have achieved state-of-the-art results in many natural language processing tasks. Although ANNs do not require manually engineered features, ANNs have many hyperparameters to be optimized.…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
Not being able to understand and predict the behavior of deep learning systems makes it hard to decide what architecture and algorithm to use for a given problem. In science and engineering, modeling is a methodology used to understand…
Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…
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…
Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach…
Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…
Meta-learning is a powerful approach that exploits historical data to quickly solve new tasks from the same distribution. In the low-data regime, methods based on the closed-form posterior of Gaussian processes (GP) together with Bayesian…
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…
Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we…
Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…
Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations…
To validate the safety of automated vehicles (AV), scenario-based testing aims to systematically describe driving scenarios an AV might encounter. In this process, continuous inputs such as velocities result in an infinite number of…