Related papers: Generalized Gaussian Kernel Adaptive Filtering

We investigate uncertainties in the estimation of the Hubble constant ($H_0$) arising from Gaussian Process (GP) reconstruction, demonstrating that the choice of kernel introduces systematic variations comparable to those arising from…

In this paper, we introduce an adaptive kernel method for solving the optimal filtering problem. The computational framework that we adopt is the Bayesian filter, in which we recursively generate an optimal estimate for the state of a…

We propose a Standing Wave Decomposition (SWD) approximation to Gaussian Process regression (GP). GP involves a costly matrix inversion operation, which limits applicability to large data analysis. For an input space that can be…

Computational kernel of the three-dimensional variational data assimilation (3D-Var) problem is a linear system, generally solved by means of an iterative method. The most costly part of each iterative step is a matrix-vector product with 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…

This paper introduces a general method to approximate the convolution of an arbitrary program with a Gaussian kernel. This process has the effect of smoothing out a program. Our compiler framework models intermediate values in the program…

The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on a Cartesian equispaced grid.…

Adaptive filtering algorithms operating in reproducing kernel Hilbert spaces have demonstrated superiority over their linear counterpart for nonlinear system identification. Unfortunately, an undesirable characteristic of these methods is…

Spectral mixture (SM) kernels comprise a powerful class of generalized kernels for Gaussian processes (GPs) to describe complex patterns. This paper introduces model compression and time- and phase (TP) modulated dependency structures to…

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…

Kernel methods have recently attracted resurgent interest, showing performance competitive with deep neural networks in tasks such as speech recognition. The random Fourier features map is a technique commonly used to scale up kernel…

In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques,…

We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error…

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 work, we introduce a spatio-temporal kernel for Gaussian process (GP) regression-based sound field estimation. Notably, GPs have the attractive property that the sound field is a linear function of the measurements, allowing the…

Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…

Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…

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 show that a new design criterion, i.e., the least squares on subband errors regularized by a weighted norm, can be used to generalize the proportionate-type normalized subband adaptive filtering (PtNSAF) framework. The new criterion…

Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…