Related papers: Deconditional Downscaling with Gaussian Processes

In this paper, we investigate the recovery of the sparse representation of data in general infinite-dimensional optimization problems regularized by convex functionals. We show that it is possible to define a suitable non-degeneracy…

Apart from discriminative models for classification and object detection tasks, the application of deep convolutional neural networks to basic research utilizing natural imaging data has been somewhat limited; particularly in cases where a…

Data collected by the Interstellar Boundary Explorer (IBEX) satellite, recording heliospheric energetic neutral atoms (ENAs), exhibit a phenomenon that has caused space scientists to revise hypotheses about the physical processes, and…

We undertake Bayesian learning of the high-dimensional functional relationship between a system parameter vector and an observable, that is in general tensor-valued. The ultimate aim is Bayesian inverse prediction of the system parameters,…

We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…

To improve the classification performance in the context of hyperspectral image processing, many works have been developed based on two common strategies, namely the spatial-spectral information integration and the utilization of neural…

Gaussian processes (GPs) have been extensively utilized as nonparametric models for component separation in 21 cm data analyses. This exploits the distinct spectral behavior of the cosmological and foreground signals, which are modeled…

In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based…

We consider supervised dimension reduction problems, namely to identify a low dimensional projection of the predictors $\-x$ which can retain the statistical relationship between $\-x$ and the response variable $y$. We follow the idea of…

It is common, in deconvolution problems, to assume that the measurement errors are identically distributed. In many real-life applications, however, this condition is not satisfied and the deconvolution estimators developed for…

This note studies the worst-case recovery error of low-rank and bisparse matrices as a function of the number of one-bit measurements used to acquire them. First, by way of the concept of consistency width, precise estimates are given on…

We investigate the conditional distributions of two Banach space valued, jointly Gaussian random variables. In particular, we show that these conditional distributions are again Gaussian and that their means and covariances can be…

Climate change exacerbates extreme weather events like heavy rainfall and flooding. As these events cause severe socioeconomic damage, accurate high-resolution simulation of precipitation is imperative. However, existing Earth System Models…

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…

Hyperspectral images (HSIs) are inevitably degraded by a mixture of various types of noise, such as Gaussian noise, impulse noise, stripe noise, and dead pixels, which greatly limits the subsequent applications. Although various denoising…

We consider the problem of learning mixtures of generalized linear models (GLM) which arise in classification and regression problems. Typical learning approaches such as expectation maximization (EM) or variational Bayes can get stuck in…

We propose a robust Bayesian formulation of random feature (RF) regression that accounts explicitly for prior and likelihood misspecification via Huber-style contamination sets. Starting from the classical equivalence between…

In this work, we investigate the estimation of a parameter $f$ in PDEs using Bayesian procedures, and focus on posterior distributions constructed using Gaussian process priors, and its variational approximation. We establish contraction…

To this day, accurately simulating local-scale precipitation and reliably reproducing its distribution remains a challenging task. The limited horizontal resolution of Global Climate Models is among the primary factors undermining their…

In this article, we study Bayesian inverse problems with multi-layered Gaussian priors. We first describe the conditionally Gaussian layers in terms of a system of stochastic partial differential equations. We build the computational…