Related papers: Algorithms for envelope estimation
The envelope of an elliptical Gaussian complex vector, or equivalently, the amplitude or norm of a bivariate normal random vector has application in many weather and signal processing contexts. We explicitly characterize its distribution in…
We investigate approximation algorithms for several fundamental optimization problems on geometric packing. The geometric objects considered are very generic, namely $d$-dimensional convex fat objects. Our main contribution is a versatile…
This paper surveys and evaluates some popular state of the art methods for algorithmic curvature and normal estimation. In addition to surveying existing methods we also propose a new method for robust curvature estimation and evaluate it…
A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation-maximization…
The envelope theory, also known as the auxiliary field method, is a simple technique to compute approximate solutions of Hamiltonians for $N$ identical particles in $D$-dimension. The accuracy of this method is tested by computing the…
Huber regression (HR) is a popular robust alternative to the least squares regression when the error follows a heavy-tailed distribution. We propose a new method called the enveloped Huber regression (EHR) by considering the envelope…
The envelope theory, also known as the auxiliary field method, is a simple technique to compute approximate solutions of Hamiltonians for $N$ identical particles in $D$ dimensions. The quality of the approximate eigenvalues can be improved…
We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.
This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is…
We review the literature on algorithms for estimating the index space in a multi-index model. The primary focus is on computationally efficient (polynomial-time) algorithms in Gaussian space, the assumptions under which consistency is…
In this paper, we introduce a Grasp Manifold Estimator (GraspME) to detect grasp affordances for objects directly in 2D camera images. To perform manipulation tasks autonomously it is crucial for robots to have such graspability models of…
An efficient algorithm to enumerate the vertices of a two-dimensional (2D) projection of a polytope, is presented in this paper. The proposed algorithm uses the support function of the polytope to be projected and enumerated for vertices.…
In a recent Letter [1] a framework for estimating entropy was introduced and applied to one-dimensional and two-dimensional systems. In this Comment we show that the method is not well suited for estimating entropy in bidimensional systems…
Estimation algebras have been extensively studied in Euclidean space, where finite-dimensional estimation algebras form the foundation of the Kalman and Benes filters, and have contributed to the discovery of many other finite-dimensional…
Aiming at abundant scientific and engineering data with not only high dimensionality but also complex structure, we study the regression problem with a multidimensional array (tensor) response and a vector predictor. Applications include,…
A flag is a sequence of nested subspaces. Flags are ubiquitous in numerical analysis, arising in finite elements, multigrid, spectral, and pseudospectral methods for numerical PDE; they arise in the form of Krylov subspaces in matrix…
Prediction performance does not always reflect the estimation behaviour of a method. High error in estimation may necessarily not result in high prediction error, but can lead to an unreliable prediction if test data lie in a slightly…
The envelope theory is an easy-to-use approximation method to obtain eigensolutions for some quantum many-body systems, in particular in the domain of hadronic physics. Even if the solutions are reliable and an improvement procedure exists,…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambient space. Our framework accommodates manifolds with…