Abstract:
I will describe a general framework of inferring a hidden basis from
imperfect measurements.
It turns out that a number of problems from the classical
eigendecompositions of symmetric matrices to
such topics of recent interest as multiclass spectral clustering,
Independent Component Analysis and
certain problems in Gaussian mixture learning can be viewed as examples
of hidden basis learning.
I will then describe algorithms for basis recovery and provide
theoretical guarantees in terms of
computational complexity and perturbation size. The proposed
algorithms are based on what may be called "gradient iteration"
and are simple to describe and to implement. They can be viewed as
generalizations of both the classical power method for recovering
eigenvectors of symmetric matrices as well as the recent work on power
methods for tensors. Unlike these methods, our analysis is based not
on the tensorial properties, but on certain "hidden convexity" of
contrast functions.
Joint work with L. Rademacher and J. Voss. |