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New Algorithms for Learning Incoherent and Overcomplete Dictionaries

New Algorithms for Learning Incoherent and Overcomplete Dictionaries

This video was recorded at 27th Annual Conference on Learning Theory (COLT), Barcelona 2014. In sparse recovery we are given a matrix A∈Rn×m ("the dictionary") and a vector of the form AX where X is sparse, and the goal is to recover X. This is a central notion in signal processing, statistics and machine learning. But in applications such as sparse coding, edge detection, compression and super resolution, the dictionary A is unknown and has to be learned from random examples of the form Y=AX where X is drawn from an appropriate distribution - this is the dictionary learning problem. In most settings, A is overcomplete: it has more columns than rows. This paper presents a polynomial-time algorithm for learning overcomplete dictionaries; the only previously known algorithm with provable... Show More

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