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Phase transition in PCA with missing data: Reduced signal-to-noise ratio, not sample size!
Niels Ipsen · Lars Kai Hansen

Wed Jun 12 03:10 PM -- 03:15 PM (PDT) @ Room 103

How does missing data affect our ability to learn signal structures? It has been shown that learning signal structure in terms of principal components is dependent on the ratio of sample size and dimensionality and that a critical number of observations is needed before learning starts (Biehl and Mietzner, 1993). Here we generalize this analysis to include missing data. Probabilistic principal component analysis is regularly used for estimating signal structures in datasets with missing data. Our analytic result suggest that the effect of missing data is to effectively reduce signal-to-noise ratio rather than - as generally believed - to reduce sample size. The theory predicts a phase transition in the learning curves and this is indeed found both in simulation data and in real datasets.

Author Information

Niels Ipsen (Technical University of Denmark)
Lars Kai Hansen (Technical University of Denmark)

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