BIRS Workshop Lecture Videos
Principal Inertia Components & Applications Salamatian, Salman
We will discuss Principal Inertia Components (PICs), a theoretical framework to finely decompose the joint distribution between two random variables X and Y. The dÃ©bute of PICs under different guises can be traced back to the works of Hirschfeld(1935), Gebelein (1941), and RÃ©nyi (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 MÃ©dard (MIT), Hsiang Hsu, and Flavio Calmon (Harvard).
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