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Abstract: Through incorporating a priori information available in some applications for independent component analysis (ICA) as the reference into the negentropy contrast function for FastICA, ICA with reference (ICA-R) or constrained ICA (cICA) is obtained as a constrained optimization problem. ICA-R achieves some advantages over earlier methods, whereas its computation load is somewhat high and its performance is strongly dependent on the threshold parameter. By alternately optimizing the negentropy contrast function for FastICA and the closeness measure for ICA-R, an improved method for ICA-R is proposed in this paper which can avoid the inherent drawbacks of ICA-R. The validity of the proposed method is demonstrated by simulation experiments. [Copyright &y& Elsevier]

Abstract: The task of estimating causal effects from non-experimental data is notoriously difficult and unreliable. Nevertheless, precisely such estimates are commonly required in many fields including economics and social science, where controlled experiments are often impossible. Linear causal models (structural equation models), combined with an implicit normality (Gaussianity) assumption on the data, provide a widely used framework for this task. We have recently described how non-Gaussianity in the data can be exploited for estimating causal effects. In this paper we show that, with non-Gaussian data, causal inference is possible even in the presence of hidden variables (unobserved confounders), even when the existence of such variables is unknown a priori. Thus, we provide a comprehensive and complete framework for the estimation of causal effects between the observed variables in the linear, non-Gaussian domain. Numerical simulations demonstrate the practical implementation of the proposed method, with full Matlab code available for all simulations. [Copyright &y& Elsevier]

Abstract: The Gaussian distribution is the least structured from the information-theoretic point of view. In this paper, projection pursuit is used to find non-Gaussian projections to explore the clustering structure of the data. We use kurtosis as a measure of non-Gaussianity to find the projection directions. Kurtosis is well known to be sensitive to influential points/outliers, and so the projection direction will be greatly affected by unusual points. We also develop the influence functions of projection directions to investigate abnormal observations. A data example illustrates the application of these approaches. [Copyright &y& Elsevier]