Related papers: Two Dimensional Density Estimation using Smooth In…
Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression problem. The advantage is that we…
We introduce a method for calculating the probability density function (PDF) of a turbulent density field in three dimensions using only information contained in the projected two-dimensional column density field. We test the method by…
We consider the convolution model where i.i.d. random variables $X_i$ having unknown density $f$ are observed with additive i.i.d. noise, independent of the $X$'s. We assume that the density $f$ belongs to either a Sobolev class or a class…
We tackle the problem of the estimation of the level sets L_f({\lambda}) of the density f of a random vector X supported on a smooth manifold M\subsetR^d , from an iid sample of X. To do that we introduce a kernel-based estimator f^n,h ,…
We derive a formula to calculate the local change to the log of any density of states for smooth real observables. Using this in Monte-Carlo simulations, we are able to calculate the expectation value of the observable with a precision…
A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly…
Stress and strain fields in a two-dimensional pixelwise disordered system are computed by a Fast Fourier Transform method. The system, a model for a ductile damaged medium, consists of an elastic-perfectly matrix containing void pixels. Its…
This paper studies the high-dimensional quantile regression problem under the transfer learning framework, where possibly related source datasets are available to make improvements on the estimation or prediction based solely on the target…
This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…
While the problem of estimating a probability density function (pdf) from its observations is classical, the estimation under additional shape constraints is both important and challenging. We introduce an efficient, geometric approach for…
Smoothing classifiers and probability density functions with Gaussian kernels appear unrelated, but in this work, they are unified for the problem of robust classification. The key building block is approximating the $\textit{energy…
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…
We build confidence balls for the common density $s$ of a real valued sample $X_1,...,X_n$. We use resampling methods to estimate the projection of $s$ onto finite dimensional linear spaces and a model selection procedure to choose an…
We provide a two dimensional deformation model to describe how soft squishy circular particles respond to external forces and collisions. This model involves formulating mathematical equations and algorithms for the shape of a deformed…
Let X be a projective smooth irreducible polarized variety over the field of complex numbers. Typical examples of wide extensions are vector bundles E that have a subsheaf F whose slope is much bigger than the slope of E/F, and such that F…
While spherical data arises in many contexts, including in directional statistics, the current tools for density estimation and population comparison on spheres are quite limited. Popular approaches for comparing populations (on Euclidean…
We develop a numerical approach for computing the additive, multiplicative and compressive convolution operations from free probability theory. We utilize the regularity properties of free convolution to identify (pairs of) `admissible'…
A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear…
Density estimation plays a crucial role in many data analysis tasks, as it infers a continuous probability density function (PDF) from discrete samples. Thus, it is used in tasks as diverse as analyzing population data, spatial locations in…
In this paper, we introduce an innovative testing procedure for assessing individual hypotheses in high-dimensional linear regression models with measurement errors. This method remains robust even when either the X-model or Y-model is…