相关论文: Kernel Selection for Gaussian Process in Cosmology…

The use of Gaussian Processes with a measurement of the cosmic expansion rate based solely on the observation of cosmic chronometers provides a completely cosmology-independent reconstruction of the Hubble constant H(z) suitable for testing…

Kernel-based machine learning approaches are gaining increasing interest for exploring and modeling large dataset in recent years. Gaussian process (GP) is one example of such kernel-based approaches, which can provide very good performance…

We propose a representation of Gaussian processes (GPs) based on powers of the integral operator defined by a kernel function, we call these stochastic processes integral Gaussian processes (IGPs). Sample paths from IGPs are functions…

A number of recent analyses of cosmological data have reported hints for the presence of extra radiation beyond the standard model expectation. In order to test the robustness of these claims under different methods of constructing…

Gaussian processes (GP) are widely used as a metamodel for emulating time-consuming computer codes. We focus on problems involving categorical inputs, with a potentially large number L of levels (typically several tens), partitioned in G <<…

Gaussian processes (GPs) are powerful probabilistic models that define flexible priors over functions, offering strong interpretability and uncertainty quantification. However, GP models often rely on simple, stationary kernels which can…

In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…

In convolutional neural networks, the convolutions are conventionally performed using a square kernel with a fixed N $\times$ N receptive field (RF). However, what matters most to the network is the effective receptive field (ERF) that…

We combine recent long Gamma Ray Bursts (GRBs) sample including 52 objects out to z$=$6.3 compiled from Swift Gamma Ray Bursts by Schaefer (2006) with Type Ia Supernova (SNIa), Cosmic Microwave Background (CMB) and Baryon Oscillation (BAO)…

Uncertainty estimation is essential for robust decision-making in the presence of ambiguous or out-of-distribution inputs. Gaussian Processes (GPs) are classical kernel-based models that offer principled uncertainty quantification and…

The search for primordial gravitational waves in the Cosmic Microwave Background (CMB) will soon be limited by our ability to remove the lensing contamination to $B$-mode polarization. The often-used quadratic estimator for lensing is known…

We study how the posterior contraction rate under a Gaussian process (GP) prior depends on the intrinsic dimension of the predictors and the smoothness of the regression function. An open question is whether a generic GP prior that does not…

Kernel selection plays a central role in determining the performance of Gaussian Process (GP) models, as the chosen kernel determines both the inductive biases and prior support of functions under the GP prior. This work addresses the…

A detection or non detection of primordial non--Gaussianity (NG) by using the cosmic microwave background radiation (CMB) is a possible way to break the degeneracy of early universe models. Since a single statistical estimator hardly can be…

In this article we investigate the effects of conformal transformations on kernel functions used in Support Vector Machines. Our focus lies in the task of text document categorization, which involves assigning each document to a particular…

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 present a method to constrain galaxy parameters directly from three-dimensional data cubes. The algorithm compares directly the data with a parametric model mapped in $x,y,\lambda$ coordinates. It uses the spectral lines-spread function…

A popular method for likelihood-free inference is approximate Bayesian computation sequential Monte Carlo (ABC-SMC) algorithms. These approximate the posterior using a population of particles, which are updated using Markov kernels. Several…

Many sources contribute to the diffuse gamma-ray background (DGRB), including star forming galaxies, active galactic nuclei, and cosmic ray interactions in the Milky Way. Exotic sources, such as dark matter annihilation, may also make some…

We use simulated maps of the cosmic microwave background anisotropy to quantify the ability of different statistical tests to discriminate between Gaussian and non-Gaussian models. Despite the central limit theorem on large angular scales,…