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HANNU OJA - University of Turku

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Third and Fourth Cumulants in Independent Component Analysis
14 April 2015 from 4:00 PM to 5:00 PM
201 Thomas Bldg.
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The independent component model is  a latent variable model where the components of the observed random vectors are linear combination of  latent independent variables. The aim is then to find an estimate for a transformation matrix back to independent components. In engineering literature, third moments are often  neglected in favour of fourth moments, even though both approaches have similar appealing properties. This paper considers the joint use of third and fourth cumulants in finding independent components. First, univariate cumulants are used as projection indices in search for independent components (projection pursuit). Second, multivariate  cumulant matrices are jointly used to solve the problem. The properties of the estimates are considered in detail through corresponding optimization problems,  estimating equations, algorithms  and asymptotic statistical properties. Comparisons of the asymptotic variances of the estimates in wide independent component models show that in most cases projection pursuit approach outperforms its competitors.

Based on joint work with Joni Virta and Klaus Nordhausen.

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