Related papers: Approximating the covariance ellipsoid

Many models of interest in the natural and social sciences have no closed-form likelihood function, which means that they cannot be treated using the usual techniques of statistical inference. In the case where such models can be…

In this paper, we present an analytical approach for the synthesis of ellipsoidal probabilistic reachable sets of saturated systems subject to unbounded additive noise. Using convex optimization methods, we compute a contraction factor of…

In [Sau11,SPW13], Saunderson, Parrilo and Willsky asked the following elegant geometric question: what is the largest $m= m(d)$ such that there is an ellipsoid in $\mathbb{R}^d$ that passes through $v_1, v_2, \ldots, v_m$ with high…

We study information projections with respect to statistical $f$-divergences between any two location-scale families. We consider a multivariate generalization of the location-scale families which includes the elliptical and the spherical…

This paper is the first in a set that analyses the covariance matrices of clustering statistics obtained from several approximate methods for gravitational structure formation. We focus here on the covariance matrices of anisotropic…

[Abridged] We seek approximations to the cosmic shear covariance that are as easy to use as the common approximations based on normal statistics, but yield more accurate covariance matrices and parameter errors. We derive expressions for…

Statistical modeling of spatiotemporal phenomena often requires selecting a covariance matrix from a covariance class. Yet standard parametric covariance families can be insufficiently flexible for practical applications, while…

We develop an randomized approximation algorithm for the size of set union problem $\arrowvert A_1\cup A_2\cup...\cup A_m\arrowvert$, which given a list of sets $A_1,...,A_m$ with approximate set size $m_i$ for $A_i$ with $m_i\in…

The least squares (LS) estimate is the archetypical solution of linear regression problems. The asymptotic Gaussianity of the scaled LS error is often used to construct approximate confidence ellipsoids around the LS estimate, however, for…

We study the k-route cut problem: given an undirected edge-weighted graph G=(V,E), a collection {(s_1,t_1),(s_2,t_2),...,(s_r,t_r)} of source-sink pairs, and an integer connectivity requirement k, the goal is to find a minimum-weight subset…

This paper addresses the problem of finding a B-term wavelet representation of a given discrete function $f \in \real^n$ whose distance from f is minimized. The problem is well understood when we seek to minimize the Euclidean distance…

The reassembling of a simple connected graph G = (V,E) is an abstraction of a problem arising in earlier studies of network analysis. The reassembling process has a simple formulation (there are several equivalent formulations) relative to…

Randomized approximation algorithms for many #P-complete problems (such as the partition function of a Gibbs distribution, the volume of a convex body, the permanent of a $\{0,1\}$-matrix, and many others) reduce to creating random…

We study the circumradius of the intersection of an $m$-dimensional ellipsoid $\mathcal E$ with semi-axes $\sigma_1\geq\dots\geq \sigma_m$ with random subspaces of codimension $n$. We find that, under certain assumptions on $\sigma$, this…

This paper derives the elliptical matrix variate version of the well known univariate Birnbaum and Saunders distribution. A generalisation based on a matrix transformation is proposed, instead of the independent element by element…

Multi-dimensional distributions of discrete data that resemble ellipsoids arise in numerous areas of science, statistics, and computational geometry. We describe a complete algebraic algorithm to determine the quadratic form specifying the…

This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local…

Fine stratification is a popular design as it permits the stratification to be carried out to the fullest possible extent. Some examples include the Current Population Survey and National Crime Victimization Survey both conducted by the…

We present a novel method for deciding whether a given n-dimensional ellipsoid contains another one (possibly with a different center). This method consists in constructing a particular concave function and deciding whether it has any value…

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…