Related papers: Finite-Sample Analysis of Fixed-k Nearest Neighbor…
In the kernel density estimation (KDE) problem, we are given a set $X$ of data points in $\mathbb{R}^d$, a kernel function $k: \mathbb{R}^d \times \mathbb{R}^d \rightarrow \mathbb{R}$, and a query point $\mathbf{q} \in \mathbb{R}^d$, and…
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…
We propose a general framework for end-to-end learning of data structures. Our framework adapts to the underlying data distribution and provides fine-grained control over query and space complexity. Crucially, the data structure is learned…
This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…
We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive…
kNN based ensemble methods minimise the effect of outliers by identifying a set of data points in the given feature space that are nearest to an unseen observation in order to predict its response by using majority voting. The ordinary…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…
The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…
In the present work, we introduce a Self-Consistent Density-Functional Embedding technique, which leaves the realm of standard energy-functional approaches in Density Functional Theory and targets directly the density-to-potential mapping…
Non-linear aggregation strategies have recently been proposed in response to the problem of how to combine, in a non-linear way, estimators of the regression function (see for instance \cite{biau:16}), classification rules (see…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
In the $k$-nearest neighborhood model ($k$-NN), we are given a set of points $P$, and we shall answer queries $q$ by returning the $k$ nearest neighbors of $q$ in $P$ according to some metric. This concept is crucial in many areas of data…
The k-nearest neighbors (kNN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between…
A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…
We consider nonparametric estimation of the mean and covariance functions for functional/longitudinal data. Strong uniform convergence rates are developed for estimators that are local-linear smoothers. Our results are obtained in a unified…
Jittering estimators are nonparametric function estimators for mixed data. They extend arbitrary estimators from the continuous setting by adding random noise to discrete variables. We give an in-depth analysis of the jittering kernel…
Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability…
Two-sample feature selection is the problem of finding features that describe a difference between two probability distributions, which is a ubiquitous problem in both scientific and engineering studies. However, existing methods have…