### DIMACS Theoretical Computer Science Seminar

Title: Uniqueness of Tensor Decompositions with Applications to Learning Latent Variable Models

Speaker: **Aravindan Vijayaraghavan**, CMU

Date: Wednesday, September 11, 2013 11:00-12:00pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

We give a robust version of the celebrated result of Kruskal on the uniqueness of tensor decompositions: we prove that given a tensor whose decomposition satisfies a robust form of fairly general condition called the Kruskal's rank condition, it is possible to recover the terms of the decomposition if the tensor is known up to a sufficiently small (inverse polynomial) error.

Kruskal's theorem has found many applications in statistics, signal processing, data mining -- in machine learning, it is used in proving the identifiability of parameters for various latent variable models and mixture models such as Hidden Markov models, mixtures of Gaussians etc. Our robust version immediately implies identifiability using only polynomially many samples in many of these settings. Given the importance of Kruskal's theorem in the tensor literature, we expect that this robust version will have several applications beyond the settings we explore in this work.

Based on joint work with Aditya Bhaskara and Moses Charikar

See: http://www.math.rutgers.edu/~sk1233/theory-seminar/F13/