Abstract
The lasso problem, least squares with a ℓ1 regularization penalty, has been very successful as a tool for obtaining sparse representations of data in terms of given dictionary. It is known, but not widely appreciated, that the lasso problem need not have a unique solution. Sufficient conditions which ensure uniqueness of the solution are known but necessary and sufficient conditions have been elusive. We present three structural results on the lasso problem. First, we show that when the dictionary has more columns than rows, it is always possible to ensure that the dictionary has full row rank. Next we show that the feasible set for the dual lasso problem is bounded if and only if the dictionary has full row rank. Lastly, we give necessary and sufficient conditions for the uniqueness of a lasso solution.
Original language | English (US) |
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Title of host publication | 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings |
Pages | 3392-3396 |
Number of pages | 5 |
DOIs | |
State | Published - Oct 18 2013 |
Event | 2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Vancouver, BC, Canada Duration: May 26 2013 → May 31 2013 |
Other
Other | 2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 |
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Country/Territory | Canada |
City | Vancouver, BC |
Period | 5/26/13 → 5/31/13 |
All Science Journal Classification (ASJC) codes
- Software
- Signal Processing
- Electrical and Electronic Engineering