def _update_beta_jac_bcd(X,
y,
beta,
dbeta,
dual_var,
ddual_var,
alpha,
L,
compute_jac=True):
n_samples, n_features = X.shape
non_zeros = np.where(L != 0)[0]
for j in non_zeros:
beta_old = beta[j]
if compute_jac:
dbeta_old = dbeta[j, :].copy()
# compute derivatives
zj = beta[j] + dual_var @ X[:, j] / (L[j] * n_samples)
beta[j] = prox_elasticnet(zj, alpha[0] / L[j], alpha[1] / L[j])
if compute_jac:
dzj = dbeta[j, :] + X[:, j] @ ddual_var / (L[j] * n_samples)
dbeta[j:j+1, :] = (1 / (1 + alpha[1] / L[j])) * \
np.abs(np.sign(beta[j])) * dzj
dbeta[j:j + 1,
0] -= (alpha[0] *
np.sign(beta[j])) / L[j] / (1 + alpha[1] / L[j])
dbeta[j:j + 1,
1] -= (alpha[1] / L[j] * beta[j]) / (1 + alpha[1] / L[j])
# update residuals
ddual_var[:, 0] -= X[:, j] * (dbeta[j, 0] - dbeta_old[0])
ddual_var[:, 1] -= X[:, j] * (dbeta[j, 1] - dbeta_old[1])
dual_var -= X[:, j] * (beta[j] - beta_old)
def _update_beta_jac_bcd_sparse(data,
indptr,
indices,
y,
n_samples,
n_features,
beta,
dbeta,
dual_var,
ddual_var,
alphas,
L,
compute_jac=True):
non_zeros = np.where(L != 0)[0]
for j in non_zeros:
# get the j-st column of X in sparse format
Xjs = data[indptr[j]:indptr[j + 1]]
# get the non zero indices
idx_nz = indices[indptr[j]:indptr[j + 1]]
beta_old = beta[j]
if compute_jac:
dbeta_old = dbeta[j, :].copy()
zj = beta[j] + dual_var[idx_nz] @ Xjs / (L[j] * n_samples)
beta[j:j + 1] = prox_elasticnet(zj, alphas[0] / L[j],
alphas[1] / L[j])
if compute_jac:
dzj = dbeta[j, :] + Xjs @ ddual_var[idx_nz, :] / \
(L[j] * n_samples)
dbeta[j:j+1, :] = (1 / (1 + alphas[1] / L[j])) * \
np.abs(np.sign(beta[j])) * dzj
dbeta[j:j+1, 0] -= alphas[0] * \
np.sign(beta[j]) / L[j] / (1 + (alphas[1] / L[j]))
dbeta[j:j + 1,
1] -= (alphas[1] / L[j] * beta[j]) / (1 +
(alphas[1] / L[j]))
# update residuals
ddual_var[idx_nz, 0] -= Xjs * (dbeta[j, 0] - dbeta_old[0])
ddual_var[idx_nz, 1] -= Xjs * (dbeta[j, 1] - dbeta_old[1])
dual_var[idx_nz] -= Xjs * (beta[j] - beta_old)