DATAIA Seminar | « Phase transition in PCA with missing data: reduced signal-to-noise ratio, not sample size! » - Lars Kai Hansen
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.
N. Ipsen, L.K. Hansen. Phase transition in PCA with missing data; Proc. ICML 2019; PMLR 97:2951-2960, 2019.
Lars Kai Hansen has MSc and PhD degrees in physics from University of Copenhagen. Since 1990 he has been with the Technical University of Denmark, where he currently heads the Section for Cognitive Systems. He has published more than 300 contributoins on machine learning, signal processing, and applications in AI and cognitive systems. His research has been generously funded by the Danish Research Councils and private foundations, the European Union, and the US National Institutes of Health. He has made seminal contributions to machine learning including the introduction of ensemble methods('90) and to functional neuroimaging including the first brain state decoding work based on PET('94) and fMRI('97). In the context of neuroimaging he has developed a suite of methods for visualizing machine learning models and quantification of uncertainty. In 2011 he was elected “Catedra de Excelencia” at UC3M Madrid, Spain.
The seminar will take place on November 27 from 3pm to 4pm at the Inria-Saclay Center - Alan Turing building - Amphitheatre Sophie Germain.
Registration free but mandatory within the limit of available seats.
A coffee break will be served before the seminar (2.30pm)
For security reasons, no access to the conference room for unregistered participants
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