Related papers: Optimizing large-scale structure data analysis wit…
We study the accuracy with which cosmological parameters can be determined from real space power spectrum of matter density contrast at weakly nonlinear scales using analytical approaches. From power spectra measured in $N$-body simulations…
Miminizing errors of the physical parameters of interest should be the ultimate goal of any event selection optimization in high energy physics data analysis involving parameter determination. Quick and reliable error estimation is a…
Selecting an optimal subset of features or instances under an information theoretic criterion has become an effective preprocessing strategy for reducing data complexity while preserving essential information. This study investigates two…
The growth rate of large-scale structure provides a powerful consistency test of the standard cosmological model and a probe of possible deviations from general relativity. We use a Fisher analysis to forecast constraints on the growth rate…
Consider the use of $\ell_{1}/\ell_{\infty}$-regularized regression for joint estimation of a $\pdim \times \numreg$ matrix of regression coefficients. We analyze the high-dimensional scaling of $\ell_1/\ell_\infty$-regularized quadratic…
This paper focuses on block likelihood estimation for geostatistical data, a method that balances statistical accuracy and computational efficiency. Central to this approach is the choice of block size, which can significantly impact…
Mixture models are a popular tool in model-based clustering. Such a model is often fitted by a procedure that maximizes the likelihood, such as the EM algorithm. At convergence, the maximum likelihood parameter estimates are typically…
Understanding generalization in deep learning has been one of the major challenges in statistical learning theory over the last decade. While recent work has illustrated that the dataset and the training algorithm must be taken into account…
Power-law probability distributions arise often in the social and natural sciences. Statistics have been developed for estimating the exponent parameter as well as gauging goodness-of-fit to a power law. Yet paradoxically, many famous power…
There is a significant gap between our theoretical understanding of optimization algorithms used in deep learning and their practical performance. Theoretical development usually focuses on proving convergence guarantees under a variety of…
Upcoming galaxy surveys will allow us to probe the growth of the cosmic large-scale structure with improved sensitivity compared to current missions, and will also map larger areas of the sky. This means that in addition to the increased…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
With the violation of the assumption of homoskedasticity, least squares estimators of the variance become inefficient and statistical inference conducted with invalid standard errors leads to misleading rejection rates. Despite a vast…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
The disconnected part of the power spectrum covariance matrix (also known as the "Gaussian" covariance) is the dominant contribution on large scales for galaxy clustering and weak lensing datasets. The presence of a complicated sky mask…
Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…
We investigate the imprints of the Generalized Uncertainty Principle on cosmological scales by using redshift-space distortion measurements in combination with background cosmological data to determine constraints on the deformation…
Structured covariance matrix estimation in the presence of missing data is addressed in this paper with emphasis on radar signal processing applications. After a motivation of the study, the array model is specified and the problem of…
Accurate platform localization is an integral component of most robotic systems. As these robotic systems become more ubiquitous, it is necessary to develop robust state estimation algorithms that are able to withstand novel and…
This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are…