Related papers: A flexible method for estimating luminosity functi…
We introduce kernel density machines (KDM), an agnostic kernel-based framework for learning the Radon-Nikodym derivative (density) between probability measures under minimal assumptions. KDM applies to general measurable spaces and avoids…
We are interested in the nonparametric estimation of the probability density of price returns, using the kernel approach. The output of the method heavily relies on the selection of a bandwidth parameter. Many selection methods have been…
We discuss and compare various approaches to the problem of bandwidth selection for kernel estimators of intensity functions of spatial point processes. We also propose a new method based on the Campbell formula applied to the reciprocal…
AI computation in healthcare faces significant challenges when clinical datasets are limited and heterogeneous. Integrating datasets from multiple sources and different equipments is critical for effective AI computation but is complicated…
Several rapid parameter estimation methods have recently been advanced to deal with the computational challenges of the problem of Bayesian inference of the properties of compact binary sources detected in the upcoming science runs of the…
Neural networks have been widely used as predictive models to fit data distribution, and they could be implemented through learning a collection of samples. In many applications, however, the given dataset may contain noisy samples or…
Stellar membership determination of an open cluster is an important process to do before further analysis. Basically, there are two classes of membership determination method: parametric and non-parametric. In this study, an alternative of…
A Local Orthogonal Polynomial Expansion (LOrPE) of the empirical density function is proposed as a novel method to estimate the underlying density. The estimate is constructed by matching localized expectation values of orthogonal…
This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…
Discovering governing equations from data is important to many scientific and engineering applications. Despite promising successes, existing methods are still challenged by data sparsity and noise issues, both of which are ubiquitous in…
We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…
The quest for a formula that satisfactorily measures the effective degrees of freedom in kernel density estimation (KDE) is a long standing problem with few solutions. Starting from the orthogonal polynomial sequence (OPS) expansion for the…
Inference of transfer operators from data is often formulated as a classical problem that hinges on the Ulam method. The conventional description, known as the Ulam-Galerkin method, involves projecting onto basis functions represented as…
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…
The extensive catalog of $\gamma$-ray selected flat-spectrum radio quasars (FSRQs) produced by \emph{Fermi} during a four-year survey has generated considerable interest in determining their $\gamma$-ray luminosity function (GLF) and its…
Probability Density Estimation (PDE) is a multivariate discrimination technique based on sampling signal and background densities defined by event samples from data or Monte-Carlo (MC) simulations in a multi-dimensional phase space. In this…
Predictive hotspot mapping plays a critical role in hotspot policing. Existing methods such as the popular kernel density estimation (KDE) do not consider the temporal dimension of crime. Building upon recent works in related fields, this…
The probability distribution of precipitation amount strongly depends on geography, climate zone, and time scale considered. Closed-form parametric probability distributions are not sufficiently flexible to provide accurate and universal…
We show that using either the method of Page & Carrera or the well-known $1/V_a$ method to construct the binned luminosity function (LF) of a flux limited sample of Active Galactic Nuclei (AGN) can produce an artificial flattening (or…
We propose a nonparametric method to learn the L\'evy density from probability density data governed by a nonlocal Fokker-Planck equation. We recast the problem as identifying the kernel in a nonlocal integral operator from discrete data,…