869

A Note on the Uniqueness of the Lasso Solution

Alessando Rinaldo

Abstract:

In this note we show that, if $\beta_1$ and $\beta_2$ are two distinct solutions to the lasso problem $\m{min}_{\beta \in \mathbb{R}^p} \Vert y - X \beta\Vert^2_2 + \lambda \Vert \beta \Vert _1$ for some $n \times p$ matrix $\m{X}$ with $p > n$, then $\m{X} \beta_1 = \m{X} \beta_2$.

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