Related papers: Nystr\"om Kernel Stein Discrepancy
In this paper, Kernel Density Estimation (KDE) as a non-parametric estimation method is used to investigate statistical properties of nuclear spectra. The deviation to regular or chaotic dynamics, is exhibited by closer distances to Poisson…
We introduce kernel thinning, a new procedure for compressing a distribution $\mathbb{P}$ more effectively than i.i.d. sampling or standard thinning. Given a suitable reproducing kernel $\mathbf{k}_{\star}$ and $O(n^2)$ time, kernel…
The general perception is that kernel methods are not scalable, and neural nets are the methods of choice for nonlinear learning problems. Or have we simply not tried hard enough for kernel methods? Here we propose an approach that scales…
The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common…
We are interested in gradient-based Explicit Generative Modeling where samples can be derived from iterative gradient updates based on an estimate of the score function of the data distribution. Recent advances in Stochastic Gradient…
We provide the first finite-particle convergence rate for Stein variational gradient descent (SVGD), a popular algorithm for approximating a probability distribution with a collection of particles. Specifically, whenever the target…
The widespread adoption of the \emph{maximum mean discrepancy} (MMD) in goodness-of-fit testing has spurred extensive research on its statistical performance. However, recent studies indicate that the inherent structure of MMD may constrain…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ($n \gg p \gg 1$). In this regime,…
Numerical data imputation algorithms replace missing values by estimates to leverage incomplete data sets. Current imputation methods seek to minimize the error between the unobserved ground truth and the imputed values. But this strategy…
Kernel methods have achieved very good performance on large scale regression and classification problems, by using the Nystr\"om method and preconditioning techniques. The Nystr\"om approximation -- based on a subset of landmarks -- gives a…
Given $M \geq 2$ distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD) -- a parameter that quantifies the difference between the $M$ distributions. The…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…
A kernel density estimator for data on the polysphere $\mathbb{S}^{d_1}\times\cdots\times\mathbb{S}^{d_r}$, with $r,d_1,\ldots,d_r\geq 1$, is presented in this paper. We derive the main asymptotic properties of the estimator, including mean…
Kernel methods are a popular class of nonlinear predictive models in machine learning. Scalable algorithms for learning kernel models need to be iterative in nature, but convergence can be slow due to poor conditioning. Spectral…
Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful nonparametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational…
Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural…
The Nystr\"om method has long been popular for scaling up kernel methods. Its theoretical guarantees and empirical performance rely critically on the quality of the landmarks selected. We study landmark selection for Nystr\"om using…
A new goodness-of-fit test for normality in high-dimension (and Reproducing Kernel Hilbert Space) is proposed. It shares common ideas with the Maximum Mean Discrepancy (MMD) it outperforms both in terms of computation time and applicability…
We introduce $\textit{Stein transport}$, a novel methodology for Bayesian inference designed to efficiently push an ensemble of particles along a predefined curve of tempered probability distributions. The driving vector field is chosen…