121,709 research outputs found
On Quasi-Newton Forward--Backward Splitting: Proximal Calculus and Convergence
We introduce a framework for quasi-Newton forward--backward splitting
algorithms (proximal quasi-Newton methods) with a metric induced by diagonal
rank- symmetric positive definite matrices. This special type of
metric allows for a highly efficient evaluation of the proximal mapping. The
key to this efficiency is a general proximal calculus in the new metric. By
using duality, formulas are derived that relate the proximal mapping in a
rank- modified metric to the original metric. We also describe efficient
implementations of the proximity calculation for a large class of functions;
the implementations exploit the piece-wise linear nature of the dual problem.
Then, we apply these results to acceleration of composite convex minimization
problems, which leads to elegant quasi-Newton methods for which we prove
convergence. The algorithm is tested on several numerical examples and compared
to a comprehensive list of alternatives in the literature. Our quasi-Newton
splitting algorithm with the prescribed metric compares favorably against
state-of-the-art. The algorithm has extensive applications including signal
processing, sparse recovery, machine learning and classification to name a few.Comment: arXiv admin note: text overlap with arXiv:1206.115
Analysis of a Custom Support Vector Machine for Photometric Redshift Estimation and the Inclusion of Galaxy Shape Information
Aims: We present a custom support vector machine classification package for
photometric redshift estimation, including comparisons with other methods. We
also explore the efficacy of including galaxy shape information in redshift
estimation. Support vector machines, a type of machine learning, utilize
optimization theory and supervised learning algorithms to construct predictive
models based on the information content of data in a way that can treat
different input features symmetrically.
Methods: The custom support vector machine package we have developed is
designated SPIDERz and made available to the community. As test data for
evaluating performance and comparison with other methods, we apply SPIDERz to
four distinct data sets: 1) the publicly available portion of the PHAT-1
catalog based on the GOODS-N field with spectroscopic redshifts in the range , 2) 14365 galaxies from the COSMOS bright survey with photometric band
magnitudes, morphology, and spectroscopic redshifts inside , 3) 3048
galaxies from the overlap of COSMOS photometry and morphology with 3D-HST
spectroscopy extending to , and 4) 2612 galaxies with five-band
photometric magnitudes and morphology from the All-wavelength Extended Groth
Strip International Survey and .
Results: We find that SPIDER-z achieves results competitive with other
empirical packages on the PHAT-1 data, and performs quite well in estimating
redshifts with the COSMOS and AEGIS data, including in the cases of a large
redshift range (). We also determine from analyses with both the
COSMOS and AEGIS data that the inclusion of morphological information does not
have a statistically significant benefit for photometric redshift estimation
with the techniques employed here.Comment: Submitted to A&A, 11 pages, 10 figures, 1 table, updated to version
in revisio
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