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The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…

This paper presents a comprehensive study of nonparametric estimation techniques on the circle using Fej\'er polynomials, which are analogues of Bernstein polynomials for periodic functions. Building upon Fej\'er's uniform approximation…

The performance of multivariate kernel density estimation (KDE) depends strongly on the choice of bandwidth matrix. The high computational cost required for its estimation provides a big motivation to develop fast and accurate methods. One…

In kernel methods, the median heuristic has been widely used as a way of setting the bandwidth of RBF kernels. While its empirical performances make it a safe choice under many circumstances, there is little theoretical understanding of why…

Distributed estimation in the context of sensor networks is considered, where distributed agents are given a set of sensor measurements, and are tasked with estimating a target variable. A subset of sensors are assumed to be faulty. The…

We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…

We construct a family of estimators for a regression function based on a sample following a qdistribution. Our approach is nonparametric, using kernel methods built from operations that leverage the properties of q-calculus. Furthermore,…

Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…

Analyzing the structure of sampled features from an input data distribution is challenging when constrained by limited measurements in both the number of inputs and features. Traditional approaches often rely on the eigenvalue spectrum of…

In this paper we propose an automatic selection of the bandwidth of the semi-recursive kernel estimators of a regression function defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and some…

We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work…

Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…

In randomized controlled trials without interference, regression adjustment is widely used to enhance the efficiency of treatment effect estimation. This paper extends this efficiency principle to settings with network interference, where a…

The problem of learning functions over spaces of probabilities - or distribution regression - is gaining significant interest in the machine learning community. A key challenge behind this problem is to identify a suitable representation…

In this paper we establish the uniform in bandwidth consistency for the transformation kernel estimator of copulas introduced in [Omelka et al.(2009)]. To this end, we first prove a uniform in bandwidth law of the iterated logarithm for the…

Kernels are key in machine learning for modeling interactions. Unfortunately, brute-force computation of the related kernel sums scales quadratically with the number of samples. Recent Fourier-slicing methods lead to an improved linear…

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…

In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…

A nonparametric method is proposed for estimating the quantile spectra and cross-spectra introduced in Li (2012; 2014) as bivariate functions of frequency and quantile level. The method is based on the quantile discrete Fourier transform…

We generalize a method for proving uniform in bandwidth consistency results for kernel type estimators developed by the two last named authors. Such results are shown to be useful in establishing consistency of local polynomial estimators…