Table 3.

Measures of Performance

Measure	Formula
Model fit
True‐positive rate (TPR)	$|\widehat{S}\in S_0|/|S_0|$
False‐positive rate (TPR)	$|\widehat{S}\notin S_0|/|j\notin S_0|$
Correct sparsity (Witten, Shojaie, & Zhang, 2014)	${\displaystyle \frac{1}{p}\sum _{j=1}^p{A}_j}$ $A_j=\left\{\begin{array}{c}1\text{if}\widehat{{\beta }_j}={\beta }_j=0\hfill \\ 1\text{if}\widehat{{\beta }_j}\ne 0,{\beta }_j\ne 0\hfill \\ 0\text{if}\text{else}\hfill \end{array}\right.$
Prediction accuracy
Root mean squared error (RMSE)	${‖{\mathbf{Y}}_{test}-\widehat{\mathit{\mu }}({\mathbf{X}}_{test})‖}_2$
Area under the curve (AUC)	Trapezoidal rule
Hosmer–Lemeshow test ($G=10$)	χ2 test statistic
Feature stability using K‐fold cross‐validation on training set (Kalousis, Prados, & Hilario, 2007)
Pearson Correlation (ρ) (Pearson, 1895)	${\displaystyle {\left(\genfrac{}{}{0pt}{}{K}{2}\right)}^{-1}\sum _{i,j\in \left\{1,\dots ,K\right\},i\ne j}\frac{cov({\widehat{\beta }}_{(i)},{\widehat{\beta }}_{(j)})}{{\sigma }_{{\widehat{\beta }}_{(i)}}{\sigma }_{{\widehat{\beta }}_{(j)}}}}$
Spearman Correlation (r) (Spearman, 1904)	${\displaystyle {\left(\genfrac{}{}{0pt}{}{K}{2}\right)}^{-1}\sum _{i,j\in \left\{1,\dots ,K\right\},i\ne j}\left[{\displaystyle 1-6\sum _m\frac{{(r_{m_{(i)}}-r_{m_{(j)}})}^2}{p(p^2-1)}}\right]}$
Jaccard Distance (Jaccard, 1912)	$\frac{|{\widehat{S}}_{(i)}\cap {\widehat{S}}_{(j)}|}{|{\widehat{S}}_{(i)}\cup {\widehat{S}}_{(j)}|}$

 $\widehat{\mathit{\mu }}$: fitting procedure on the training set.

 S ₀: index of active set $=\left\{j;{\beta }_j^0\ne 0\right\}$.

 $\widehat{S}$: index of the set of nonzero estimated coefficients $=\left\{j;{\widehat{\beta }}_j\ne 0\right\}$.

 $|A|$: is the cardinality of set A.