Cédric Beny (Perimeter Institute/University of Hanover): Dimensionality reduction from coarse-grained Fisher metric

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Date(s) - 22/05/2015
14 h 00 min - 15 h 00 min

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Title: Dimensionality reduction from coarse-grained Fisher metric\n\nAbstract: In physics\, one is often interested in describing only the large-scale\nproperties of complex statistical states. Renormalisation is the\nproblem of finding the most relevant variables for that purpose. I\nwill show how a method developed in that context can be used for the\ndimensional reduction of abstract data. The approach yields a “PCA\nkernel” whose diagonalisation amounts to finding the perturbations of\nthe empirical distribution whose distinguishability is least affected\nby a certain noise model (coarse-graining). This approach is invariant\nunder arbitrary changes of coordinates. The kernel\, however\, requires\nthe calculation of a partition function which must be approximated. I\npresent two numerical examples.

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