An Approximate Inference Approach for the PCA Reconstruction Error

Part of Advances in Neural Information Processing Systems 18 (NIPS 2005)

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Manfred Opper


The problem of computing a resample estimate for the reconstruction error in PCA is reformulated as an inference problem with the help of the replica method. Using the expectation consistent (EC) approximation, the intractable inference problem can be solved efficiently using only two variational parameters. A perturbative correction to the result is computed and an alternative simplified derivation is also presented.