Abstract
Group Lasso is Lasso such that the variables are categorized into K groups \(k=1,\ldots ,K\). The \(p_k\) variables \(\theta _k=[\theta _{1,k},\ldots ,\theta _{p_k,k}]^T\in {\mathbb R}^{p_k}\) in the same group share the same times at which the nonzero coefficients become zeros when we increase the \(\lambda \) value. This chapter considers groups with nonzero and zero coefficients to be active and nonactive, respectively, for each \(\lambda \). In other words, group Lasso chooses active groups rather than active variables. The active and nonactive status may be different among the groups.
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Notes
- 1.
Nesterov’s accelerated gradient method (2007) [22].
- 2.
If there exists \(m>0\) such that \((\nabla f(x)-\nabla f(y))^T(x-y)\ge \frac{m}{2}\Vert x-y\Vert ^2\) for arbitrary \(x,y\in {\mathbb R}\), then we say that \(f: {\mathbb R}\rightarrow {\mathbb R}\) is strongly convex. In this case, the error can be exponentially decreased w.r.t. k (Nesterov, 2007).
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The hitters of the Yomiuri Giants, Japan, each of which has at least one opportunity to bat.
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Suzuki, J. (2021). Group Lasso. In: Sparse Estimation with Math and R. Springer, Singapore. https://doi.org/10.1007/978-981-16-1446-0_3
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DOI: https://doi.org/10.1007/978-981-16-1446-0_3
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