Independent Component Analysis by Wavelets
Résumé
We propose an ICA contrast based on density estimation of the observed signal and its marginal distributions through wavelets. The statistical risk of the wavelet contrast is linked with approximation properties in Besov spaces. Follows a discussion on computational issues; in particular, we resort to dyadic rational approximations to compute wavelet coefficients, instead of the usual histogram and filter scheme generally used in density estimation. The implemented wavelet contrast has linear complexity in n; numerical simulations give results as good as those of existing methods, if no better. The wavelet contrast also admits explicit differentials; using a simple jackknife, we give filter aware and computationally tractable formulations for the gradient and hessian of the contrast estimator.