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

Masahiro Yukawa, Shun Ichi Amari

研究成果: Conference contribution

4 被引用数 (Scopus)

抄録

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).

本文言語English
ホスト出版物のタイトル2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012
ページ2221-2225
ページ数5
DOI
出版ステータスPublished - 2012 10 22
外部発表はい
イベント2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States
継続期間: 2012 7 12012 7 6

出版物シリーズ

名前IEEE International Symposium on Information Theory - Proceedings

Other

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

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 情報システム
  • モデリングとシミュレーション
  • 応用数学

フィンガープリント

「ℓ <sub>p</sub>-constrained least squares (0 < p < 1) and its critical path」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル