Algorithm 2.

Cross Validation

Require:
fε	{smooth model function}
𝒮ε	{smooth regularizer function}
β0	{initial guess}
d	{data}
λj	{regularization parameter}
1: choose n cross validation sample sets {di}i=1, …,n
2: for i = 1 to n do
3:    extract sub-sample set
4:    ${\mathit{\beta ̂}}_j^n={\text{arg min}}_{\mathit{\beta }}{f}_{\epsilon }(\mathit{\beta })+{𝒮}_{\epsilon }(\lambda j,\mathit{\beta })$ using di
{optimization method see Algorithm 1}
5:    calculate $f_i=f_{\epsilon }({\mathit{\beta }}_i^n)$
6: end for
7: calculate Vj = mean (fi’s)
Ensure:
Vj