Related papers: Kernel Mean Estimation and Stein's Effect
This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing…
Batch normalization (BN) is a ubiquitous operation in deep neural networks, primarily used to improve stability and regularization during training. BN centers and scales feature maps using sample means and variances, which are naturally…
The mean shift algorithm is a popular way to find modes of some probability density functions taking a specific kernel-based shape, used for clustering or visual tracking. Since its introduction, it underwent several practical improvements…
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…
Mean-field control problems have received continuous interest over the last decade. Despite being more intricate than in classical optimal control, the linear-quadratic setting can still be tackled through Riccati equations. Remarkably, we…
This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…
We propose a nonparametric statistical test for goodness-of-fit: given a set of samples, the test determines how likely it is that these were generated from a target density function. The measure of goodness-of-fit is a divergence…
As a promising step, the performance of data analysis and feature learning are able to be improved if certain pattern matching mechanism is available. One of the feasible solutions can refer to the importance estimation of instances, and…
We establish a link between Fourier optics and a recent construction from the machine learning community termed the kernel mean map. Using the Fraunhofer approximation, it identifies the kernel with the squared Fourier transform of the…
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…
With the widespread application of causal inference, it is increasingly important to have tools which can test for the presence of causal effects in a diverse array of circumstances. In this vein we focus on the problem of testing for…
Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…
For a larger set of predictions of several differently trained machine learning models, known as bagging predictors, the mean of all predictions is taken by default. Nevertheless, this proceeding can deviate from the actual ground truth in…
Kernel methods underpin many of the most successful approaches in data science and statistics, and they allow representing probability measures as elements of a reproducing kernel Hilbert space without loss of information. Recently, the…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
We consider kernel estimators of the instantaneous frequency of a slowly evolving sinusoid in white noise. The expected estimation error consists of two terms. The systematic bias error grows as the kernel halfwidth increases while the…
We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…
We determine the expected error by smoothing the data locally. Then we optimize the shape of the kernel smoother to minimize the error. Because the optimal estimator depends on the unknown function, our scheme automatically adjusts to the…
Data in non-Euclidean spaces are commonly encountered in many fields of Science and Engineering. For instance, in Robotics, attitude sensors capture orientation which is an element of a Lie group. In the recent past, several researchers…
In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…