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 language | English |
|---|---|
| Title of host publication | IEEE International Symposium on Information Theory - Proceedings |
| Pages | 2221-2225 |
| Number of pages | 5 |
| DOIs | |
| Publication status | Published - 2012 |
| Externally published | Yes |
| Event | 2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States Duration: 2012 Jul 1 → 2012 Jul 6 |
Other
| Other | 2012 IEEE International Symposium on Information Theory, ISIT 2012 |
|---|---|
| Country | United States |
| City | Cambridge, MA |
| Period | 12/7/1 → 12/7/6 |
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ASJC Scopus subject areas
- Applied Mathematics
- Modelling and Simulation
- Theoretical Computer Science
- Information Systems
Cite this
ℓ 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 proceeding › Conference contribution
}
TY - GEN
T1 - ℓ p-constrained least squares (0 < p < 1) and its critical path
AU - Yukawa, Masahiro
AU - Amari, Shun Ichi
PY - 2012
Y1 - 2012
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=84867496879&partnerID=8YFLogxK
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U2 - 10.1109/ISIT.2012.6283848
DO - 10.1109/ISIT.2012.6283848
M3 - Conference contribution
AN - SCOPUS:84867496879
SN - 9781467325790
SP - 2221
EP - 2225
BT - IEEE International Symposium on Information Theory - Proceedings
ER -