Holy and Nemenman, 2002

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T Holy and I Nemenman. On impossibility of learning in a reparameterization covariant way. Technical Report NSF-KITP-03-123, KITP, UCSB, 2002. PDF.

The paper proves that reparameterization covariant learning of a probability density function of a continuous variable is impossible. Further, we suggest a tradeoff between approximate reparameterization covariance and generalization, similar to the classical bias-variance tradeoff.