Related papers: A Unified MDL-based Binning and Tensor Factorizati…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
This article addresses the different methods of estimation of the probability density function (PDF) and the cumulative distribution function (CDF) for the Lindley distribution. Following estimation methods are considered: uniformly minimum…
In this paper, we consider distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic…
The current PDF4LHC recommendation to estimate uncertainties due to parton distribution functions (PDFs) in theoretical predictions for LHC processes involves the combination of separate predictions computed using PDF sets from different…
Modern analysis on parton distribution functions (PDFs) requires calculations of the log-likelihood functions from thousands of experimental data points, and scans of multi-dimensional parameter space with tens of degrees of freedom. In…
Modeling large dependent datasets in modern time series analysis is a crucial research area. One effective approach to handle such datasets is to transform the observations into density functions and apply statistical methods for further…
A probability density function (PDF) of a spatially dependent field provides a means of calculating moments of the field or, equivalently, the proportion of a spatial domain that is mapped to a given set of values. This paper describes a…
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…
This paper proposes a comprehensive and unprecedented framework that streamlines the derivation of exact, compact -- yet tractable -- solutions for the probability density function (PDF) and cumulative distribution function (CDF) of the sum…
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…
Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…
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 fundamental role in many areas of statistics and machine learning. Parametric, nonparametric and semiparametric density estimation methods have been proposed in the literature. Semiparametric density models are…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
Quantitatively connecting properties of parton distribution functions (PDFs, or parton densities) to the theoretical assumptions made within the QCD analyses which produce them has been a longstanding problem in HEP phenomenology. To…
We propose a novel approach for density estimation called histogram trend filtering. Our estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. We begin by showing…
A robust uncertainty estimate in global analyses of Parton Distribution Functions (PDFs) is essential at the Large Hadron Collider (LHC), especially in view of the high-precision data anticipated by experimentalists in the High-Luminosity…
Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…
Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of…
If two probability density functions (PDFs) have values for their first $n$ moments which are quite close to each other (upper bounds of their differences are known), can it be expected that the PDFs themselves are very similar? Shown below…