Séminaire DATAIA avec Lars Kai Hansen
Dans le cadre de son animation scientifique, l'Institut DATAIA organise des séminaires visant à échanger autour de l'IA.
- Date : 27/11/2019
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Principal component analysis (PCA) is widely used, easy to formulate and compute - yet has many surprising behaviors! It has been shown that the performance of PCA depends on the signal-to-noise ratio and on the ratio of sample size-to-dimensionality. Since the early 90s it is also known that a critical sample size is needed before learning occurs (Biehl and Mietzner, 1993). Here we generalize this analysis to include missing data. An analytic result suggest that the effect of missingdata is to effectively reduce signal-to-noise rather than - as commonly believed - to reduce sample size. The theory predicts a phase transition induced by the missingprocess and this is indeed observed in simulated and in real data.