Related papers: Optimizing Gaussian Process Kernels Using Nested S…
In this paper we investigate a link between state- space models and Gaussian Processes (GP) for time series modeling and forecasting. In particular, several widely used state- space models are transformed into continuous time form and…
Gaussian processes (GPs) are Bayesian non-parametric models popular in a variety of applications due to their accuracy and native uncertainty quantification (UQ). Tuning GP hyperparameters is critical to ensure the validity of prediction…
In the context of the discrepancies between the early and late universe, we emphasize the importance of independent measurements of the cosmic curvature in the late universe. We present an investigation of the model-independent measurement…
We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…
In this work, we reconstruct the Hubble diagram using various data sets, including correlated ones, in Artificial Neural Networks (ANN). Using ReFANN, that was built for data sets with independent uncertainties, we expand it to include…
Gaussian processes provide a method for extracting cosmological information from observations without assuming a cosmological model. We carry out cosmography -- mapping the time evolution of the cosmic expansion -- in a model-independent…
Many three-dimensional spatial fields are anisotropic, with directions of rapid and slow variation that need not align with the coordinate axes. Standard Gaussian process kernels with Automatic Relevance Determination (ARD) capture only…
Strong gravitational lenses provide source/lens distance ratios D_obs useful in cosmological tests. Previously, a catalog of 69 such systems was used in a one-on-one comparison between the standard model, LCDM, and the R_h=ct universe,…
This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact…
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…
Modern cosmological surveys such as the Hyper Suprime-Cam (HSC) survey produce a huge volume of low-resolution images of both distant galaxies and dim stars in our own galaxy. Being able to automatically classify these images is a…
Bayesian optimization with Gaussian processes (GP) is commonly used to optimize black-box functions. The Mat\'ern and the Radial Basis Function (RBF) covariance functions are used frequently, but they do not make any assumptions about the…
In this work, we achieve the determination of the cosmic curvature $\Omega_K$ in a cosmological model-independent way, by using the Hubble parameter measurements $H(z)$ and type Ia supernovae (SNe Ia). In our analysis, two nonlinear…
Many applications in speech, robotics, finance, and biology deal with sequential data, where ordering matters and recurrent structures are common. However, this structure cannot be easily captured by standard kernel functions. To model such…
We propose a novel class of Gaussian processes (GPs) whose spectra have compact support, meaning that their sample trajectories are almost-surely band limited. As a complement to the growing literature on spectral design of covariance…
Gaussian Processes (GPs) are highly expressive, probabilistic models. A major limitation is their computational complexity. Naively, exact GP inference requires $\mathcal{O}(N^3)$ computations with $N$ denoting the number of modeled points.…
Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…
Kernel models of potential energy surfaces (PES) for polyatomic molecules are often restricted by a specific choice of the kernel function. This can be avoided by optimizing the complexity of the kernel function. For regression problems…
We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…
We reconstruct the Hubble function from cosmic chronometers, supernovae, and baryon acoustic oscillations compiled data sets via the Gaussian process (GP) method and use it to draw out Horndeski theories that are fully anchored on expansion…