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vignettes/pen_est.Rmd
@@ -40,19 +40,19 @@ Consider the following setting:
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## Sparse-Group Estimator
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-\begin{gather}
+\begin{align}
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\hat{\Omega}(\lambda,\alpha,\gamma)
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= \operatorname*{arg\,min}_{\Omega \succ 0} \Bigl\{
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- \log\det(\Omega) + \operatorname{tr}(S\Omega)
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-+ P_{\lambda,\alpha,\gamma}(\Omega) \Bigr\}, \\ \\
++ P_{\lambda,\alpha,\gamma}(\Omega) \Bigr\}, \\
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P_{\lambda,\alpha,\gamma}(\Omega)
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= \alpha P^\text{individual}_{\lambda,\gamma}(\Omega)
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-+ (1-\alpha) P^\text{group}_{\lambda,\gamma}(\Omega), \\ \\
++ (1-\alpha) P^\text{group}_{\lambda,\gamma}(\Omega), \\
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P^\text{individual}_{\lambda,\gamma}(\Omega)
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-= \sum_{i,j} p_{\lambda,\gamma}(\vert\omega_{ij}\vert), \\ \\
+= \sum_{i,j} p_{\lambda,\gamma}(\vert\omega_{ij}\vert), \\
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P^\text{group}_{\lambda,\gamma}(\Omega)
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= \sum_{g,g^\prime} p_{\lambda,\gamma}(\Vert\Omega_{gg^\prime}\Vert_F),
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-\end{gather}
+\end{align}
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where:
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