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Guest Lecture by Professor Lars Kai Hansen, DTU


18.06.2019 kl. 14.00 - 15.00


“Phase transition in PCA with missing data: Reduced signal-to-noise ratio, not sample size!”


Prof. Lars Kai Hansen
Technical University of Denmark

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 has been known that a critical sample size is needed before learning occurs (Biehl and Mietzner, 1993). Here we generalize this analysis to include missing data.  The analytic result suggest that the effect of missing data 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 missing process and this is indeed found both in simulations and real data.

Paper: Niels Ipsen, Lars Kai Hansen; Proc. of the 36th International Conference on Machine Learning, PMLR 97:2951-2960, 2019 (http://proceedings.mlr.press/v97/ipsen19a.html)

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 heads the Section for Cognitive Systems. He has published more than 300 contributions 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.

All are welcome!


free of charge


Signal and Information Processing , Department of Electronic Sysrtems


Aalborg University, Fredrik Bajers Vej 7, A4-108

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