Lasso 560-8531 1-3 $E$ -mail: hirose@sigmath.es.osaka-u.ac.jp. $L_{1}$ $L_{1}$ $L_{1}$ 1 $L_{1}$ $L_{1}$ $0$ $0$ $L_{1}$ $L_{1}$ $L_{1}$ Lasso (Least absolute shrinkage and selection operator, Tibshirani 1996) (Friedman et al. 2010) (Zhao and Yu 2007) $p$ $(x_{1}, . . . , xp)$ $y$ $N$ $\{(y_{i}, x_{i1}, \ldots, x_{ip});i=1, . . . , N\}$ $y_{i}= \beta_{0}+\sum_{j=1}^{p}\beta_{j}x_{ij}+\epsilon_{i},