Related papers: Robust density estimation over star-shaped density…
This paper tackles a fundamental inference problem: given $n$ observations from a distribution $P$ over $\mathbb{R}^d$ with unknown mean $\boldsymbol{\mu}$, we must form a confidence set for the index (or indices) corresponding to the…
Motivated by the orthogonal series density estimation in $L^2([0,1],\mu)$, in this project we consider a new class of functions that we call the approximate sparsity class. This new class is characterized by the rate of decay of the…
We study the problem of recovering an $s$-sparse signal $\mathbf{x}^{\star}\in\mathbb{C}^n$ from corrupted measurements $\mathbf{y} = \mathbf{A}\mathbf{x}^{\star}+\mathbf{z}^{\star}+\mathbf{w}$, where $\mathbf{z}^{\star}\in\mathbb{C}^m$ is…
State-of-the-art cosmological hydrodynamical simulations of galaxy formation have reached the point at which their outcomes result in galaxies with ever more realism. Still, the employed sub-grid models include several free parameters such…
We present initial results on the use of Mixture Models for density estimation in large astronomical databases. We provide herein both the theoretical and experimental background for using a mixture model of Gaussians based on the…
We consider the estimation of the global mode of a density under some decay rate condition around the global mode. We show that the maximum of a histogram, with proper choice of bandwidth, achieves the minimax rate that we establish for the…
We develop an eigenspace estimation algorithm for distributed environments with arbitrary node failures, where a subset of computing nodes can return structurally valid but otherwise arbitrarily chosen responses. Notably, this setting…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
The most common approach to mitigate the impact that the presence of malicious nodes has on the accuracy of decision fusion schemes consists in observing the behavior of the nodes over a time interval T and then removing the reports of…
The relations between star formation and properties of molecular clouds are studied based on a sample of star forming regions in the Galactic Plane. Sources were selected by having radio recombination lines to provide identification of…
Newborn stars form within the localized, high density regions of molecular clouds. The sequence and rate at which stars form in dense clumps and the dependence on local and global environments are key factors in developing descriptions of…
Reducing the scatter between cluster mass and optical richness is a key goal for cluster cosmology from photometric catalogs. We consider various modifications to the red-sequence matched filter richness estimator of Rozo et al. (2009), and…
Robust covariance estimation is the following, well-studied problem in high dimensional statistics: given $N$ samples from a $d$-dimensional Gaussian $\mathcal{N}(\boldsymbol{0}, \Sigma)$, but where an $\varepsilon$-fraction of the samples…
Stars form in molecular complexes that are visible as giant clouds ($\sim 10^{5-6} \mathrm{M}_\odot$) in nearby galaxies and as giant clumps ($\sim 10^{8-9}\mathrm{M}_\odot$) in galaxies at redshifts $z\approx1$$-$$3$. Theoretical…
We consider estimating the predictive density under Kullback-Leibler loss in an $\ell_0$ sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable…
We study the construction of coresets for kernel density estimates. That is we show how to approximate the kernel density estimate described by a large point set with another kernel density estimate with a much smaller point set. For…
We consider a finite mixture of Gaussian regression model for high- dimensional data, where the number of covariates may be much larger than the sample size. We propose to estimate the unknown conditional mixture density by a maximum…
We measure the stellar mass surface densities of early type galaxies by observing the micro-lensing of macro-lensed quasars caused by individual stars, including stellar remnants, brown dwarfs and red dwarfs too faint to produce photometric…
This paper studies the problem of recovering a signal vector and the corrupted noise vector from a collection of corrupted linear measurements through the solution of a l1 minimization, where the sensing matrix is a partial Fourier matrix…
A mixture density, $f_p,$ is estimable in $R^d, \ d \ge 1,$ but an estimate for the mixing density, $p,$ is usually obtained only when $d$ is unity; $h$ is the mixture's kernel. When $f_p$'s estimate has form $f_{\hat p_n}$ and $p$ is…