相关论文: Orthogonally Decoupled Variational Fourier Feature…

Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…

We present a dimension-incremental method for function approximation in bounded orthonormal product bases to learn the solutions of various differential equations. Therefore, we decompose the source function of the differential equation…

Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…

Existing feature selection methods fail to properly account for interactions between features when evaluating feature subsets. In this paper, we attempt to remedy this issue by using orthogonal variance decomposition to evaluate features.…

Sparse Gaussian processes and various extensions thereof are enabled through inducing points, that simultaneously bottleneck the predictive capacity and act as the main contributor towards model complexity. However, the number of inducing…

We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…

We introduce a new class of inter-domain variational Gaussian processes (GP) where data is mapped onto the unit hypersphere in order to use spherical harmonic representations. Our inference scheme is comparable to variational Fourier…

We provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased…

A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…

High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The analysis of variance (ANOVA) decomposition and the anchored decomposition are typical techniques to find…

We present a novel method for stochastic interpolation of sparsely sampled time signals based on a superstatistical random process generated from a multivariate Gaussian scale mixture. In comparison to other stochastic interpolation methods…

In this paper, we consider multiple signals sharing same instantaneous frequencies. This kind of data is very common in scientific and engineering problems. To take advantage of this special structure, we modify our data-driven…

Approximating field variables and data vectors from sparse samples is a key challenge in computational science. Widely used methods such as gappy proper orthogonal decomposition and empirical interpolation rely on linear approximation…

We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…

We develop a fast variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. Our approach enables uncertainty in covariance function…

Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

This article focuses on covariance estimation for multi-study data. Popular approaches employ factor-analytic terms with shared and study-specific loadings that decompose the variance into (i) a shared low-rank component, (ii)…

This study introduces pre-orthogonal adaptive Fourier decomposition (POAFD) to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli and Silvestre…

In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the…