p-constrained least squares (0 < p < 1) and its critical path

Masahiro Yukawa, Shun Ichi Amari

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

The ℓ p-constrained least squares, which is denoted by (Pc), for 0 < p < 1 is addressed. A maximal continuous curve of its critical solutions β(c) for different bounds c forms a critical path which can be constructed with the variational method. The path is a piecewise smooth single-valued function of c, containing non-optimal points such as saddle points and local maxima in general as well as global minima. The path of global minima may coincide with a critical path but may jump from a critical path to another one. The breakpoints of the greedy path (a critical path constructed with a certain greedy selection criterion) coincide with the step-by-step solutions generated by the orthogonal matching pursuit (OMP). A critical point of (Pc) is also a critical point of the ℓ p-penalized least squares (Q λ) which reformulates (P c) with the Lagrangian multiplier. The greedy path is a multi-valued function of λ and is formed by a collection of multiple critical paths of (Q λ).

Original languageEnglish
Title of host publicationIEEE International Symposium on Information Theory - Proceedings
Pages2221-2225
Number of pages5
DOIs
Publication statusPublished - 2012
Externally publishedYes
Event2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States
Duration: 2012 Jul 12012 Jul 6

Other

Other2012 IEEE International Symposium on Information Theory, ISIT 2012
CountryUnited States
CityCambridge, MA
Period12/7/112/7/6

Fingerprint

Constrained Least Squares
Critical Path
Path
Global Minimum
Critical point
Penalized Least Squares
Lagrangian multiplier
Multivalued Functions
Matching Pursuit
Single valued
Saddlepoint
Variational Methods
Jump
Curve

ASJC Scopus subject areas

  • Applied Mathematics
  • Modelling and Simulation
  • Theoretical Computer Science
  • Information Systems

Cite this

Yukawa, M., & Amari, S. I. (2012). p-constrained least squares (0 < p < 1) and its critical path. In IEEE International Symposium on Information Theory - Proceedings (pp. 2221-2225). [6283848] https://doi.org/10.1109/ISIT.2012.6283848

p-constrained least squares (0 < p < 1) and its critical path. / Yukawa, Masahiro; Amari, Shun Ichi.

IEEE International Symposium on Information Theory - Proceedings. 2012. p. 2221-2225 6283848.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Yukawa, M & Amari, SI 2012, p-constrained least squares (0 < p < 1) and its critical path. in IEEE International Symposium on Information Theory - Proceedings., 6283848, pp. 2221-2225, 2012 IEEE International Symposium on Information Theory, ISIT 2012, Cambridge, MA, United States, 12/7/1. https://doi.org/10.1109/ISIT.2012.6283848
Yukawa M, Amari SI. p-constrained least squares (0 < p < 1) and its critical path. In IEEE International Symposium on Information Theory - Proceedings. 2012. p. 2221-2225. 6283848 https://doi.org/10.1109/ISIT.2012.6283848
Yukawa, Masahiro ; Amari, Shun Ichi. / p-constrained least squares (0 < p < 1) and its critical path. IEEE International Symposium on Information Theory - Proceedings. 2012. pp. 2221-2225
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