Machine Learning / Duolingo Seminar

— 11:30am

Location:
In Person and Virtual - ET - Newell-Simon 4305 and Zoom

Speaker:
RAVI KANNAN , Distinguished Scholar and Visiting Professor of Operations Research, Tepper School of Business, Carnegie Mellon University
https://www.cmu.edu/tepper/faculty-and-research/faculty-by-area/profiles/kannan-ravi.html

The Latent k polytope problem (LkP)

We show that several hidden variable problems (including Topic Models (LDA), Mixed Membership models, Clustering) can be abstracted to a geometric problem called LkP: Learn the vertices of a k vertex polytope K from observed data generated by spectrally bounded perturbations of hidden points in K, where, a fraction of hidden points lies close to each vertex of K.

We show that an intuitive algorithm finds approximations to vertices of K: Pick random directions u in the space of the top k singular vectors of data. Approximately maximize u · x over K (which we show can be done using data). We use a theorem we prove - the Random Separating Hyperplane Theorem (RSH)- to conclude that the set of maximima contains approximations to all vertices of K. RSH may be of independent interest; it strengthens the classical Separating Hyperplane Theorem for polytopes. The final piece of the algorithm is to find the k vertex approximations from the maxima, which involves a procedure called “Soft Convex Hull”.

C. Bhattacharyya, Indian Institute of Science
R. Kannan, Carnegie Mellon University
A. Kumar, Indian Institute of Technology, Delhi

In Person and Zoom Participation. See announcement.


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