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Mean absolute deviation function is used to explore the pattern and the distribution of the data graphically to enable analysts gaining greater understanding of raw data and to foster quick and a deep understanding of the data as an…
Deep Neural Networks (DNN) are core components for classification and regression tasks of many software systems. Companies incur in high costs for testing DNN with datasets representative of the inputs expected in operation, as these need…
The density profiles of dark matter halos are typically modeled using empirical formulae fitted to the density profiles of relaxed halo populations. We present a neural network model that is trained to learn the mapping from the raw density…
Conventional studies of galaxy clustering within the framework of halo models typically assume that the density profile of all dark matter haloes can be approximated by the Navarro-Frenk-White (NFW) spherically symmetric profile. However,…
Radiative transfer modeling of spectral lines including partial redistribution (PRD) effects requires the evaluation of the ratio of the emission to the absorption profile. This quantity requires a large amount of computational work if one…
The joint statistics of partial sums of ordered random variables (RVs) are often needed for the accurate performance characterization of a wide variety of wireless communication systems. A unified analytical framework to determine the joint…
We present an algorithm for testing halfspaces over arbitrary, unknown rotation-invariant distributions. Using $\tilde O(\sqrt{n}\epsilon^{-7})$ random examples of an unknown function $f$, the algorithm determines with high probability…
Quantile regression is an effective technique to quantify uncertainty, fit challenging underlying distributions, and often provide full probabilistic predictions through joint learnings over multiple quantile levels. A common drawback of…
In this paper, we address the problem of approximating a multivariate function defined on a general domain in $d$ dimensions from sample points. We consider weighted least-squares approximation in an arbitrary finite-dimensional space $P$…
The functional linear regression model has been widely studied and utilized for dealing with functional predictors. In this paper, we study the Nystr\"om subsampling method, a strategy used to tackle the computational complexities inherent…
We apply machine learning in the form of a nearest neighbor instance-based algorithm (NN) to generate full photometric redshift probability density functions (PDFs) for objects in the Fifth Data Release of the Sloan Digital Sky Survey (SDSS…
We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…
The one-point probability distribution function (PDF) of the matter density field in the universe is a fundamental property that plays an essential role in cosmology for estimates such as gravitational weak lensing, non-linear clustering,…
The first step toward doing high-precision astrometry is the measurement of individual stars in individual images, a step that is fraught with dangers when the images are undersampled. The key to avoiding systematic positional error in…
We investigate the mass profile of LambdaCDM halos using a suite of numerical simulations spanning five decades in halo mass, from dwarf galaxies to rich galaxy clusters. Our analysis confirms the proposal of Navarro, Frenk & White (NFW)…
Fast Ewald summation efficiently evaluates Coulomb interactions and is widely used in molecular dynamics simulations. It is based on a split into a short-range and a long-range part, where evaluation of the latter is accelerated using the…
The column density probability distribution function (N-PDF) of GMCs has been used as a diagnostic of star formation. Simulations and analytic predictions have suggested the N-PDF is composed of a low density lognormal component and a high…
We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval.…
We study partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained…
In this paper, we propose a Network-Weighted Functional Regression (NWFR) model, an extension of Spatially Weighted Functional Regression (SWFR) to functional data defined on network-structured settings. To asses predictive uncertainity, we…