10,314 research outputs found
Greedy Algorithms for Cone Constrained Optimization with Convergence Guarantees
Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe
(FW) algorithms regained popularity in recent years due to their simplicity,
effectiveness and theoretical guarantees. MP and FW address optimization over
the linear span and the convex hull of a set of atoms, respectively. In this
paper, we consider the intermediate case of optimization over the convex cone,
parametrized as the conic hull of a generic atom set, leading to the first
principled definitions of non-negative MP algorithms for which we give explicit
convergence rates and demonstrate excellent empirical performance. In
particular, we derive sublinear () convergence on general
smooth and convex objectives, and linear convergence () on
strongly convex objectives, in both cases for general sets of atoms.
Furthermore, we establish a clear correspondence of our algorithms to known
algorithms from the MP and FW literature. Our novel algorithms and analyses
target general atom sets and general objective functions, and hence are
directly applicable to a large variety of learning settings.Comment: NIPS 201
Oblique Matching Pursuit
A method for selecting a suitable subspace for discriminating signal
components through an oblique projection is proposed. The selection criterion
is based on the consistency principle introduced by M. Unser and A. Aldroubi
and extended by Y. Elder. An effective implementation of this principle for the
purpose of subspace selection is achieved by updating of the dual vectors
yielding the corresponding oblique projector.Comment: Last version- as it will appear in IEEE SPL. IEEE Signal Processing
Letters (in press
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