25,252 research outputs found
Overlearning in marginal distribution-based ICA: analysis and solutions
The present paper is written as a word of caution, with users of
independent component analysis (ICA) in mind, to overlearning
phenomena that are often observed.\\
We consider two types of overlearning, typical to high-order
statistics based ICA. These algorithms can be seen to maximise the
negentropy of the source estimates. The first kind of overlearning
results in the generation of spike-like signals, if there are not
enough samples in the data or there is a considerable amount of
noise present. It is argued that, if the data has power spectrum
characterised by curve, we face a more severe problem, which
cannot be solved inside the strict ICA model. This overlearning is
better characterised by bumps instead of spikes. Both overlearning
types are demonstrated in the case of artificial signals as well as
magnetoencephalograms (MEG). Several methods are suggested to
circumvent both types, either by making the estimation of the ICA
model more robust or by including further modelling of the data
Extraction of the underlying structure of systematic risk from non-Gaussian multivariate financial time series using independent component analysis: Evidence from the Mexican stock exchange
Regarding the problems related to multivariate non-Gaussianity of financial time series, i.e., unreliable results in extraction of underlying risk factors -via Principal Component Analysis or Factor Analysis-, we use Independent Component Analysis (ICA) to estimate the pervasive risk factors that explain the returns on stocks in the Mexican Stock Exchange. The extracted systematic risk factors are considered within a statistical definition of the Arbitrage Pricing Theory (APT), which is tested by means of a two-stage econometric methodology. Using the extracted factors, we find evidence of a suitable estimation via ICA and some results in favor of the APT.Peer ReviewedPostprint (published version
Stochastic trapping in a solvable model of on-line independent component analysis
Previous analytical studies of on-line Independent Component Analysis (ICA)
learning rules have focussed on asymptotic stability and efficiency. In
practice the transient stages of learning will often be more significant in
determining the success of an algorithm. This is demonstrated here with an
analysis of a Hebbian ICA algorithm which can find a small number of
non-Gaussian components given data composed of a linear mixture of independent
source signals. An idealised data model is considered in which the sources
comprise a number of non-Gaussian and Gaussian sources and a solution to the
dynamics is obtained in the limit where the number of Gaussian sources is
infinite. Previous stability results are confirmed by expanding around optimal
fixed points, where a closed form solution to the learning dynamics is
obtained. However, stochastic effects are shown to stabilise otherwise unstable
sub-optimal fixed points. Conditions required to destabilise one such fixed
point are obtained for the case of a single non-Gaussian component, indicating
that the initial learning rate \eta required to successfully escape is very low
(\eta = O(N^{-2}) where N is the data dimension) resulting in very slow
learning typically requiring O(N^3) iterations. Simulations confirm that this
picture holds for a finite system.Comment: 17 pages, 3 figures. To appear in Neural Computatio
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