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Principal Inertia Components & Applications

Banff International Research Station for Mathematical Innovation and Discovery

We will discuss Principal Inertia Components (PICs), a theoretical framework to finely decompose the joint distribution between two random variables X and Y. The débute of PICs under different guises can be traced back to the works of Hirschfeld(1935), Gebelein (1941), and Rényi (1959). We show how the PICs connect and extend various concept in Statistics and Information Theory such as Maximal Correlation, Spectral Clustering of probability graphs, and Common Information. We then present applications of this technique to problems in Privacy against inference, Correspondence Analysis at scale, and black-box model comparisons. This is joint work with: Ali Makhdoumi, Muriel Médard (MIT), Hsiang Hsu, and Flavio Calmon (Harvard).

Mathematics; Information and communication, circuits; Functional analysis; Applied computer science

video/mp4

Author affiliation: Massachusetts Institute of Technology

2019-04-30

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69994

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/