Risk estimation for matrix recovery with spectral regularization
Idioma
en
Communication dans un congrès
Este ítem está publicado en
ICML'2012 workshop on Sparsity, Dictionaries and Projections in Machine Learning and Signal Processing, 2012-06-30, Edinburgh.
Resumen en inglés
In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of the SURE theory, a key step is to compute ...Leer más >
In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of the SURE theory, a key step is to compute the (weak) derivative and divergence of a solution with respect to the observations. As such a solution is not available in closed form, but rather through a proximal splitting algorithm, we propose to recursively compute the divergence from the sequence of iterates. A second challenge that we unlocked is the computation of the (weak) derivative of the proximity operator of a spectral function. To show the potential applicability of our approach, we exemplify it on a matrix completion problem to objectively and automatically select the regularization parameter.< Leer menos
Palabras clave en inglés
Risk estimation
SURE
matrix recovery
matrix completion
matrix-valued function
spectral regularization
nuclear norm
proximal algorithms
Orígen
Importado de HalCentros de investigación