Related papers: Local Orthogonal Polynomial Expansion for Density …
In this work, we study wavelet projection estimators for density estimation, focusing on their construction from $\mathcal{S}$-regular, compactly supported wavelet bases. A key aspect of such estimators is the choice of the resolution…
We present alphaPDE, a new multivariate analysis technique for parameter estimation. The method is based on a direct construction of joint probability densities of known variables and the parameters to be estimated. We show how posterior…
The sparse polynomial approximation of continuous functions has emerged as a prominent area of interest in function approximation theory in recent years. A key challenge within this domain is the accurate estimation of approximation errors.…
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual…
The efficient estimation of an approximate model order is very important for real applications with multi-dimensional data if the observed low-rank data is corrupted by additive noise. In this paper, we present a novel robust method for…
It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation,…
We propose a novel method for density estimation that leverages an estimated score function to debias kernel density estimation (SD-KDE). In our approach, each data point is adjusted by taking a single step along the score function with a…
A mesh-free numerical method for solving linear elliptic PDE's using the local kernel theory that was developed for manifold learning is proposed. In particular, this novel approach exploits the local kernel theory which allows one to…
Conditional density estimation (CDE) models can be useful for many statistical applications, especially because the full conditional density is estimated instead of traditional regression point estimates, revealing more information about…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…
The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing…
Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…
Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…
This paper introduces a novel kernel density estimator (KDE) based on the generalised exponential (GE) distribution, designed specifically for positive continuous data. The proposed GE KDE offers a mathematically tractable form that avoids…
Real-time density estimation is ubiquitous in many applications, including computer vision and signal processing. Kernel density estimation is arguably one of the most commonly used density estimation techniques, and the use of "sliding…
The local density approximation (LDA) constructed through quantum Monte Carlo calculations of the homogeneous electron gas (HEG) is the most common approximation to the exchange-correlation functional in density functional theory. We…
Over-parameterized models like deep nets and random forests have become very popular in machine learning. However, the natural goals of continuity and differentiability, common in regression models, are now often ignored in modern…
Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…
Here we propose an algorithm, named generalized orthogonal components regression (GOCRE), to explore the relationship between a categorical outcome and a set of massive variables. A set of orthogonal components are sequentially constructed…
We introduce a broadly applicable statistical procedure for testing which parametric distribution family generated a random sample of data. The method, termed the Difference in Differential Entropy (DDE) test, provides a unified framework…