Related papers: Orthogonal Random Features: Explicit Forms and Sha…
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…
This work proposed kernel selection approaches for probabilistic classifiers based on features produced by the convolutional encoder of a variational autoencoder. Particularly, the developed methodologies allow the selection of the most…
In these lecture notes we present some connections between random matrices, the asymmetric exclusion process, random tilings. These three apparently unrelated objects have (sometimes) a similar mathematical structure, an interlacing…
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…
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…
We investigate how to train kernel approximation methods that generalize well under a memory budget. Building on recent theoretical work, we define a measure of kernel approximation error which we find to be more predictive of the empirical…
Speckle patterns are formed by random interferences of mutually coherent beams. While speckles are often considered as an unwanted noise in many areas, they also formed the foundation for the development of numerous speckle-based imaging,…
We study the approximation properties of random ReLU features through their reproducing kernel Hilbert space (RKHS). We first prove a universality theorem for the RKHS induced by random features whose feature maps are of the form of nodes…
In this paper we present a new fast and accurate method for Radial Basis Function (RBF) approximation, including interpolation as a special case, which enables us to effectively find the optimal value of the RBF shape parameter. In…
Time series data analytics has been a problem of substantial interests for decades, and Dynamic Time Warping (DTW) has been the most widely adopted technique to measure dissimilarity between time series. A number of global-alignment kernels…
In this paper, we develop a quadrature framework for large-scale kernel machines via a numerical integration representation. Considering that the integration domain and measure of typical kernels, e.g., Gaussian kernels, arc-cosine kernels,…
Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random…
This paper addresses distributed learning of a complex object for multiple networked robots based on distributed optimization and kernel-based support vector machine. In order to overcome a fundamental limitation of polynomial kernels…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision…
Kernel methods such as kernel ridge regression and Gaussian process regressions with Matern type kernels have been increasingly used, in particular, to fit potential energy surfaces (PES) and density functionals, and for materials…
In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…
Slow kinetic processes of molecular systems can be analyzed by computing dominant eigenpairs of the Koopman operator or its generator. In this context, the Variational Approach to Markov Processes (VAMP) provides a rigorous way of…
Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…
Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks in the limit of infinitely wide hidden layers by using…