Overcomplete ICA
• What if we have more independent sources than data
components? (independent \= orthogonal)
– The data no longer specifies a unique vector of
source activities. It specifies a distribution.
• This also happens if we have sensor noise in square case.
– The posterior over sources is non-Gaussian because
the prior is non-Gaussian.
• So we need to approximate the posterior:
– MCMC samples
– MAP (plus Gaussian around MAP?)
– Variational