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Accurate channel state information (CSI) is critical for current and next-generation multi-antenna systems. Yet conventional pilot-based estimators incur prohibitive overhead as antenna counts grow. In this paper, we address this challenge…
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
Gaussian processes (GP) and Kriging are widely used in traditional spatio-temporal mod-elling and prediction. These techniques typically presuppose that the data are observed from a stationary GP with parametric covariance structure.…
Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…
Automating statistical modelling is a challenging problem in artificial intelligence. The Automatic Statistician takes a first step in this direction, by employing a kernel search algorithm with Gaussian Processes (GP) to provide…
The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit…
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time…
We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a…
We examine the necessity of interpolation in overparameterized models, that is, when achieving optimal predictive risk in machine learning problems requires (nearly) interpolating the training data. In particular, we consider simple…
Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure…
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…
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…
Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…
Interpolation and prediction have been useful approaches in modeling data in many areas of applications. The aim of this paper is the prediction of the next value of a time series (time series forecasting) using the techniques in…
Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about…
We introduce scalable deep kernels, which combine the structural properties of deep learning architectures with the non-parametric flexibility of kernel methods. Specifically, we transform the inputs of a spectral mixture base kernel with a…
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…
Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are…
In several real world applications, machine learning models are deployed to make predictions on data whose distribution changes gradually along time, leading to a drift between the train and test distributions. Such models are often…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…