A practical alternating descent algorithm with data-driven initialization, momentum, homotopy continuation, and reweighting solves short-and-sparse blind deconvolution on synthetic and real imaging and neuroscience data, though without new formal recovery guarantees.
Efficient Dictionary Learning with Gradient Descent
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of poor objective value. For some highly structured nonconvex problems however, the success of gradient descent can be understood by studying the geometry of the objective. We study one such problem -- complete orthogonal dictionary learning, and provide converge guarantees for randomly initialized gradient descent to the neighborhood of a global optimum. The resulting rates scale as low order polynomials in the dimension even though the objective possesses an exponential number of saddle points. This efficient convergence can be viewed as a consequence of negative curvature normal to the stable manifolds associated with saddle points, and we provide evidence that this feature is shared by other nonconvex problems of importance as well.
fields
eess.SP 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Short-and-Sparse Deconvolution -- A Geometric Approach
A practical alternating descent algorithm with data-driven initialization, momentum, homotopy continuation, and reweighting solves short-and-sparse blind deconvolution on synthetic and real imaging and neuroscience data, though without new formal recovery guarantees.