# What does “parsimonious” property mean? (Appears in text about $l_p$ penalties in regression)

While reading a highly cited paper I found completely new terminology. Google and student-friends who are studying mathematics do not know it. Can you help please?

It appears in the discussion of $l_p$-norm penalty terms in regression.

[...] A value of $p = 2$ leads to the ridge estimate, while $p = 0$ corresponds to traditional model selection. It is well known that the estimates have a parsimonious property (with some components being exactly zero) for $p \leq 1$ only, while the optimization problem in (3) is only convex for $p \geq 1$ [...]

What does "parsimonious" mean in this context?

• It appears that the intended meaning is given in the parentheses: "parsimonious property" means that some of the coefficient estimates can be exactly zero. – markseeto Nov 30 '16 at 8:14

## 1 Answer

They are referring to the fact that $l_1$ tends to reduce coefficients to 0, so as stated in this answer:

A parsimonious model is a model that accomplishes a desired level of explanation or prediction with as few predictor variables as possible.