Accelerating cross-validation with total variation and its application to super-resolution imaging

Tomoyuki Obuchi; Shiro Ikeda; Kazunori Akiyama; Yoshiyuki Kabashima

doi:10.1371/journal.pone.0188012

Accelerating cross-validation with total variation and its application to super-resolution imaging

PLoS One. 2017 Dec 7;12(12):e0188012. doi: 10.1371/journal.pone.0188012. eCollection 2017.

Authors

Tomoyuki Obuchi¹, Shiro Ikeda², Kazunori Akiyama^{3

4

5}, Yoshiyuki Kabashima¹

Affiliations

¹ Department of Mathematical and Computing Science/Tokyo Institute of Technology, Yokohama 226-8502, Japan.
² The Institute of Statistical Mathematics, Tachikawa, Tokyo, 190-8562, Japan.
³ Haystack Observatory/Massachusetts Institute of Technology, Westford, MA, 01886, United States of America.
⁴ National Astronomy Observatory of Japan, Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan.
⁵ Black Hole Initiative, Harvard University, Cambridge, MA, 02138, United States of America.

Abstract

We develop an approximation formula for the cross-validation error (CVE) of a sparse linear regression penalized by ℓ1-norm and total variation terms, which is based on a perturbative expansion utilizing the largeness of both the data dimensionality and the model. The developed formula allows us to reduce the necessary computational cost of the CVE evaluation significantly. The practicality of the formula is tested through application to simulated black-hole image reconstruction on the event-horizon scale with super resolution. The results demonstrate that our approximation reproduces the CVE values obtained via literally conducted cross-validation with reasonably good precision.

Publication types

Validation Study

MeSH terms

Algorithms
Linear Models
Models, Theoretical*

Grants and funding

This work was supported by Japan Society for the Promotion of Science 25120008 to Prof. Shiro Ikeda; 26870185 to Dr. Tomoyuki Obuchi; 25120013 to Prof. Yoshiyuki Kabashima; 17H00764 to Dr. Tomoyuki Obuchi and Prof. Yoshiyuki Kabashima; Research Abroad Program to Dr. Kazunori Akiyama; and National Science Foundation AST-1614868 to Dr. Kazunori Akiyama.