Related papers: Interpretable deep Gaussian processes with moments
We propose a method (TT-GP) for approximate inference in Gaussian Process (GP) models. We build on previous scalable GP research including stochastic variational inference based on inducing inputs, kernel interpolation, and structure…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…
Despite the high performance of neural network-based time series forecasting methods, the inherent challenge in explaining their predictions has limited their applicability in certain application areas. Due to the difficulty in identifying…
Deep neural networks (DNNs) have demonstrated impressive performance on a wide array of tasks, but they are usually considered opaque since internal structure and learned parameters are not interpretable. In this paper, we re-examine the…
Despite the effectiveness of multitask deep neural network (MTDNN), there is a limited theoretical understanding on how the information is shared across different tasks in MTDNN. In this work, we establish a formal connection between MTDNN…
Calibrating the confidence of neural network classifiers is essential for quantifying the reliability of their predictions during inference. However, conventional Gaussian Process (GP) calibration methods often fail to capture the internal…
The wide adoption of Convolutional Neural Networks (CNNs) in applications where decision-making under uncertainty is fundamental, has brought a great deal of attention to the ability of these models to accurately quantify the uncertainty in…
Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…
We provide a definition and explicit expressions for $n$-body Gaussian Process (GP) kernels which can learn any interatomic interaction occurring in a physical system, up to $n$-body contributions, for any value of $n$. The series is…
Neural network approaches for meta-learning distributions over functions have desirable properties such as increased flexibility and a reduced complexity of inference. Building on the successes of denoising diffusion models for generative…
Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…
This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of…
Gaussian process (GP) models have received increasing attention in recent years due to their superb prediction accuracy and modeling flexibility. To address the computational burdens of GP models for large-scale datasets, distributed…
Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…
The Gaussian process state-space model (GPSSM) has garnered considerable attention over the past decade. However, the standard GP with a preliminary kernel, such as the squared exponential kernel or Mat\'{e}rn kernel, that is commonly used…
Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with…
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…
To reduce the curse of dimensionality for Gaussian processes (GP), they can be decomposed into a Gaussian Process Network (GPN) of coupled subprocesses with lower dimensionality. In some cases, intermediate observations are available within…
Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…