/**
* Returns the value of the penalty term in the elastic net regularization.
*/
double elnet_penalty(vec beta, // coefficients
double lambda, // regularization parameter
double alpha, // elastic net mixing parameter
vec penalty) // relative penalties for the variables
{
double value;
uvec fin = find_finite(penalty);
value = lambda*sum(penalty.elem(fin) % (0.5*(1-alpha)*square(beta.elem(fin))
+ alpha*(abs(beta.elem(fin))) ) );
return(value);
}
//FUNCTION SPECIFIC TO MAIN FUNCTION------------------------------------------------------
//[[Rcpp::export]]
double llmnl_con(vec const& betastar, vec const& y, mat const& X, vec const& SignRes = NumericVector::create(0)){
// Wayne Taylor 7/8/2016
// Evaluates log-likelihood for the multinomial logit model WITH SIGN CONSTRAINTS
// NOTE: this is exported only because it is used in the shell .R function, it will not be available to users
//Reparameterize betastar to beta to allow for sign restrictions
vec beta = betastar;
//The default SignRes vector is a single element vector containing a zero
//any() returns true if any elements of SignRes are non-zero
if(any(SignRes)){
uvec signInd = find(SignRes != 0);
beta.elem(signInd) = SignRes.elem(signInd) % exp(beta.elem(signInd)); //% performs element-wise multiplication
}
int n = y.size();
int j = X.n_rows/n;
mat Xbeta = X*beta;
vec xby = zeros<vec>(n);
vec denom = zeros<vec>(n);
for(int i = 0; i<n;i++){
for(int p=0;p<j;p++) denom[i]=denom[i]+exp(Xbeta[i*j+p]);
xby[i] = Xbeta[i*j+y[i]-1];
}
return(sum(xby - log(denom)));
}
//-----------------------------------------------------
// Cross-validation across an array of lambda and pick up the best.
List CV_lam_grid_cpp(vec y_vect, mat x_mat, vec id_vect, mat hat_R_full, vec beta_ini, int fold, int n, vec m, int obs_n, int p, uvec start, uvec end, vec lam_vect, double eps_tozero, double eps_stop, int iter_try){
int lam_length = lam_vect.n_elem;
double lam_temp, cv_sum, flag_stop_sum, iter_n_sum, cv_min = math::inf(), lam_min = -1;
uvec cvgrps_seq = linspace<uvec>(0, (n-1), n);
uvec cvgrps_subsets = shuffle(cvgrps_seq);
uvec cvgrps_which = cvgrps_seq - floor( cvgrps_seq / fold) * fold;
uvec index_cv_train, index_cv_test;
vec cv_vect(lam_length), flag_stop_vect(lam_length), iter_n_vect(lam_length);
uvec idx_train, idx_test;
vec y_train, y_test, id_train, m_train, beta_train;
mat x_train, x_test;
List indGen_res, beta_shrink_res;
for(int lam_iter = 0; lam_iter < lam_length; lam_iter++)
{
lam_temp = lam_vect(lam_iter);
cv_sum = 0;
flag_stop_sum = 0;
iter_n_sum = 0;
for(int k = 0; k < fold; k++)
{
index_cv_train = cvgrps_subsets.elem(find(cvgrps_which != k));
index_cv_test = cvgrps_subsets.elem(find(cvgrps_which == k));
idx_train = unique(seqJoin_vec(start.elem(index_cv_train), end.elem(index_cv_train), m.elem(index_cv_train)));
idx_test = unique(seqJoin_vec(start.elem(index_cv_test), end.elem(index_cv_test), m.elem(index_cv_test)));
y_train = y_vect.elem(idx_train);
x_train = x_mat.rows(idx_train);
id_train = id_vect.elem(idx_train);
indGen_res = indGen_cpp(id_train);
y_test = y_vect.elem(idx_test);
x_test = x_mat.rows(idx_test);
beta_shrink_res = beta_shrink_normal_cpp(y_train, x_train, id_train, hat_R_full, beta_ini, as<int>(indGen_res[0]), as<vec>(indGen_res[1]), as<int>(indGen_res[2]), p, as<uvec>(indGen_res[3]), as<uvec>(indGen_res[4]), as<vec>(indGen_res[5]), as<uvec>(indGen_res[6]), lam_temp, eps_tozero, eps_stop, iter_try);
cv_sum += sqrt(mean(pow((y_test - x_test * as<vec>(beta_shrink_res[0])),2)));
flag_stop_sum += as<double>(beta_shrink_res[2]);
iter_n_sum += as<double>(beta_shrink_res[3]);
}
// Calculate average across k-fold validation
cv_vect(lam_iter) = cv_sum / fold;
flag_stop_vect(lam_iter) = flag_stop_sum / fold;
iter_n_vect(lam_iter) = iter_n_sum / fold;
if(cv_sum < cv_min)
{
lam_min = lam_temp;
cv_min = cv_sum;
}
}
return List::create(Named("lam.vect") = lam_vect,
Named("cv.vect") = cv_vect,
Named("flag_stop_vect") = flag_stop_vect,
Named("iter_n_vect") = iter_n_vect,
Named("lam.min") = lam_min,
Named("cv.min") = cv_min
);
}
