Title: A Maximum Matching Algorithm for Basis Selection in Spectral Learning,
Abstract: We present a solution to scale spectral algorithms for learning sequence
functions. We are interested in the case where these functions are sparse (that
is, for most sequences they return 0). Spectral algorithms reduce the learning
problem to the task of computing an SVD decomposition over a special type of
matrix called the Hankel matrix. This matrix is designed to capture the
relevant statistics of the training sequences. What is crucial is that to
capture long range dependencies we must consider very large Hankel matrices.
Thus the computation of the SVD becomes a critical bottleneck. Our solution
finds a subset of rows and columns of the Hankel that realizes a compact and
informative Hankel submatrix. The novelty lies in the way that this subset is
selected: we exploit a maximal bipartite matching combinatorial algorithm to
look for a sub-block with full structural rank, and show how computation of
this sub-block can be further improved by exploiting the specific structure of
Hankel matrices.