相关论文: Deconditional Downscaling with Gaussian Processes

This paper introduces a novel variational Bayesian method that integrates Tucker decomposition for efficient high-dimensional inverse problem solving. The method reduces computational complexity by transforming variational inference from a…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

The focus of this work is the convergence of non-stationary and deep Gaussian process regression. More precisely, we follow a Bayesian approach to regression or interpolation, where the prior placed on the unknown function $f$ is a…

Obtaining high-resolution maps of precipitation data can provide key insights to stakeholders to assess a sustainable access to water resources at urban scale. Mapping a nonstationary, sparse process such as precipitation at very high…

Restricted Boltzmann machines (RBMs) are energy-based models analogous to the Ising model and are widely applied in statistical machine learning. The standard inverse Ising problem with a complete dataset requires computing both data and…

Wasserstein gradient and Hamiltonian flows have emerged as essential tools for modeling complex dynamics in the natural sciences, with applications ranging from partial differential equations (PDEs) and optimal transport to quantum…

Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large…

For many survey-based spatial modelling problems, responses are observed as spatially aggregated over survey regions due to limited resources. Covariates, from weather models and satellite imageries, can be observed at many different…

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…

In this paper, we tackle the problem of blind image super-resolution(SR) with a reformulated degradation model and two novel modules. Following the common practices of blind SR, our method proposes to improve both the kernel estimation as…

Learning expressive kernels while retaining tractable inference remains a central challenge in scaling Gaussian processes (GPs) to large and complex datasets. We propose a scalable GP regressor based on deep basis kernels (DBKs). Our DBK is…

We present an operator-free, measure-theoretic approach to the conditional mean embedding (CME) as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of unconditional distributions has…

While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic…

The fully connected conditional random field (CRF) with Gaussian pairwise potentials has proven popular and effective for multi-class semantic segmentation. While the energy of a dense CRF can be minimized accurately using a linear…

We consider the problem of multivariate density deconvolution where the distribution of a random vector needs to be estimated from replicates contaminated with conditionally heteroscedastic measurement errors. We propose a conceptually…

Gravitational lensing data is frequently collected at low resolution due to instrumental limitations and observing conditions. Machine learning-based super-resolution techniques offer a method to enhance the resolution of these images,…

Deconvolution is a fundamental inverse problem in signal processing and the prototypical model for recovering a signal from its noisy measurement. Nevertheless, the majority of model-based inversion techniques require knowledge on the…

Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient-enhanced covariance matrix can be beneficial since it provides a more…

We prove that conditional diffusion models whose reverse kernels are finite Gaussian mixtures with ReLU-network logits can approximate suitably regular target distributions arbitrarily well in context-averaged conditional KL divergence, up…

Reproducing an all-in-focus image from an image with defocus regions is of practical value in many applications, eg, digital photography, and robotics. Using the output of some existing defocus map estimator, existing approaches first…