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This paper formulates the problem of maximum likelihood subspace learning and innovation characterization in the presence of generalized Gaussian noise. This approach leads to a set of necessary conditions that are a nonlinear generalization of the Gaussian eigenvalue decomposition of the sample covariance matrix. To address the innovation problem, a class of jointly generalized Gaussian random variables is introduced using a generalized correlation matrix. Necessary condition for the maximum likelihood estimate of that matrix are derived, whose solution would permit the recovery of the innovation.