How to learn a dictionary

Thời gian: 08:30 đến 11:30 Ngày 04/01/2017

Địa điểm: C2-714

Báo cáo viên: Vũ Hà Văn

Tóm tắt:

Imagine an orchestra with hundred of instruments, but we managed to record only a few random moments.

At each of these random moments, only a small part of the instruments are playing with different intensities (we do not know which instruments and what intensity.) Can one detect all the instruments in the orchestra from the broken record ?

This is a toy description of a new and fundamental problem in machine learning theory. One needs to learn a dictionary (a collection of signals), having only a record of the mixture of only few signals at random sample points.

The question is: when and how could one reconstruct the dictionary ? Mathematically, it reduces to a problem of solving the linear equation XY= B, where X,Y, B are matrices, and we know only B.

Impossible as it sounds, the problem is actually solvable, under a mild and natural assumption.

(Based on work of Spielman, Wang, Wright 2012 and Luh and Vu 2015)

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