Blind Source Separation

Blind Source Separation consists of recovering original signals from their mixtures when the mixing process is unknown. In biomedicine, namely in MEG and EEG signal processing, one of the most popular algorithms nowadays is SOBI (Second Order Blind Identification). We proposed a procedure for fast implementation of the Weights-Adjusted SOBI (WASOBI) algorithm for asymptotically optimal separation of Gaussian autoregressive (AR) sources. The procedure employs fast computation of the optimum weight matrix, as well as an elaborate scheme for minimization of the associated weighted Least-Squares criterion. The resultant complexity is O(d²M²+d³M), where d is the number of sources and M is the required number of estimated correlation matrices. Our procedure allows separation of more than 100 sources in order of tens of seconds in Matlab. Simulations verify that the algorithm still attains the corresponding Cramér-Rao bound, even in these high dimensions.

Divergences and Informations in Statistics and Information Theory

Basic properties of f-divergences are proved in a new simpler manner. New relations to sufficiency and deficiency are established and new applications in estimation and testing are proposed. Statistical information of De Groot and the classical information of Shannon are shown to be extremal cases of a newly introduced class of so-called Arimoto informations.

Robustness of Median Estimator in Bernoulli Logistic Regression

The paper of T. Hobza and L. Pardo: On Robustness of Median Estimator in Bernoulli Logistic Regression published in the Proceedings of the Prague Stochastics 2006, presents generalized logistic regression models which include the classical model with binary responses governed by the Bernoulli law depending on the logistic regression function. The median estimator of the logistic regression parameters employing smoothed data in the discrete case, introduced in Hobza et al (2005), is considered. Sensitivity of this estimator to contaminations of the logistic regression data is studied by simulations and compared with the sensitivity of some robust estimators previously introduced to logistic regression. The median estimator is demonstrated to be more robust for higher levels of contamination.