Let X = (Xjk) denote a Hermitian random matrix with entries Xjk, which are independent for 1 ≤ j ≤ k. We consider the rate of convergence of the empirical spectral distribution function of the matrix X to the semi-circular law assuming that EXjk = 0, EX 2 jk = 1 and that the distributions of the matrix elements Xjk have a uniform sub exponential decay in the sense that there exists a constant κ...

The joint-space inertia matrix of a robot mechanism can be highly ill-conditioned. This phenomenon is not merely a numerical artifact: it is symptomatic of an underlying property of the mechanism itself that can make it more difficult to simulate or control. This paper investigates the problem by means of an empirical study of the eigenvalues, eigenvectors and condition number of the joint-spac...

The main principle of stacked generalization is using a second-level generalizer to combine the outputs of base classifiers in an ensemble. In this paper, after presenting a short survey of the literature on stacked generalization, we propose to use regularized empirical risk minimization (RERM) as a framework for learning the weights of the combiner which generalizes earlier proposals and enab...

Before we give the appendix material, we note the following: In general, all the algorithms described (both previous algorithms and those proposed in this paper) can be run either on a true preference matrix P as input (wherePij+Pji = 1 for all i 6= j) or on an empirical preference matrix P̂ as input (where there might be some (i, j) pairs for which P̂ij = P̂ji = 0). The notation P used in describ...

LetX = (Xjk) denote n×p random matrix with entriesXjk, which are independent for 1 ≤ j ≤ n, 1 ≤ k ≤ p. We consider the rate of convergence of empirical spectral distribution function of matrix W = 1 p XX ∗ to the Marchenko–Pastur law. We assume that EXjk = 0, EX 2 jk = 1 and that the distributions of the matrix elements Xjk have a uniformly sub exponential decay in the sense that there exists a...

Previously, Bottou and LeCun [1] established that the second-order stochastic gradient descent (SGD) method can potentially achieve generalization performance as well as empirical optimum in a single pass through the training examples. However, second-order SGD requires computing the inverse of the Hessian matrix of the loss function, which is usually prohibitively expensive. Recently, we inven...

This paper presents a new estimation scheme for signal processing problems in unknown noise field. The Empirical Likelihood has been introduced in the mathematical community, but, surprisingly, it is still unknown in the signal processing community. This estimation method is an alternative to estimate unknown parameters without using a model for the probability density function. The aim of this...

Let {Xij}, i, j = . . . , be a double array of i.i.d. complex random variables with EX11 = 0,E|X11| 2 = 1 and E|X11| 4 <∞, and let An = 1 N T 1/2 n XnX ∗ nT 1/2 n , where T 1/2 n is the square root of a nonnegative definite matrix Tn and Xn is the n×N matrix of the upper-left corner of the double array. The matrix An can be considered as a sample covariance matrix of an i.i.d. sample from a pop...

Recently, Chernozhukov, Chetverikov, and Kato [Ann. Statist. 42 (2014) 1564–1597] developed a new Gaussian comparison inequality for approximating the suprema of empirical processes. This paper exploits this technique to devise sharp inference on spectra of large random matrices. In particular, we show that two long-standing problems in random matrix theory can be solved: (i) simple bootstrap i...