Article history: Available online 30 July 2011

The AdaBoost algorithm of Freund and Schapire (1997) was designed to combine many “weak” hypotheses that perform slightly better than a random guess into a “strong” hypothesis that has very low error. We study the rate at which AdaBoost iteratively converges to the minimum of the “exponential loss” with a fast rate of convergence. Our proofs do not require a weak-learning assumption, nor do the...

It is known that, in the autoregressive model the spectral sensitivity curves are almost flat for the log-area ratios and in this paper it is shown that this property can be useful in adaptive IIR filtering. A new IIR lattice-form algorithm for adaptive filtering is proposed in which the update equation is applied to these parameters instead of the reflection coefficients. This transformation g...

Splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which the simple pieces of the decomposition are processed individually. This leads to easily implementable and highly parallelizable algorithms, which often obtain nearly state-of-the-art perfor...

In this paper we prove that there exists a random sequence θi for the Glimm scheme such that the approximate solution u (t) converges to the exact semigroup solution Stū of the strictly hyperbolic system of conservation laws ut + f(u)x = 0, u(t = 0) = ū as follows: for all T ≥ 0 it holds lim ε→0 ‖uε(T )− ST ū √ ε| log ε| = 0. This result is the extension of the analysis of [9] to the general ca...

We study the problem of reaching a consensus in the values of a distributed system of agents with time-varying connectivity in the presence of delays. We consider a widely studied consensus algorithm, in which at each time step, every agent forms a weighted average of its own value with values received from the neighboring agents. We study an asynchronous operation of this algorithm using delay...

This paper presents results from a project on phonetic convergence in German spontaneous speech. We used linear mixed models to examine 22 unimodal and 24 multimodal dialogs for articulation rate. We show that speakers’ local articulation rates are influenced by the preceding rates of their interlocutors, and that the direction of this influence (i.e., divergence or convergence) depends on soci...

Concave-Convex Procedure (CCCP) has been widely used to solve nonconvex d.c.(difference of convex function) programs occur in learning problems, such as sparse support vector machine (SVM), transductive SVM, sparse principal componenent analysis (PCA), etc. Although the global convergence behavior of CCCP has been well studied, the convergence rate of CCCP is still an open problem. Most of d.c....

We consider the normalized sum of n independent identically distributed random variables Xi; i = 1; : : : ; n with the common probability distribution function F (x) and probability density q(y) = F (y). We suppose that the distribution function Fn(y) of the normalized sum converges as n ! 1 to a stable distribution or stable law. The only stable distributions are the normal distributions and t...

Boosting is one of the most significant developments in machine learning. This paper studies the rate of convergence of L2Boosting, which is tailored for regression, in a high-dimensional setting. Moreover, we introduce so-called “post-Boosting”. This is a post-selection estimator which applies ordinary least squares to the variables selected in the first stage by L2Boosting. Another variant is...