def linear_pst_ridge(y, X, lam, max_iter=1000, tol=1e-7, algo="proj_gd"):
"""
This function had not been finished;
"""
n, p = X.shape
x = np.zeros(p)
XTX = np.dot(X.T, X)
XTy = np.dot(X.T, y)
ss = 1.0 / (max_eigval(
XTX, eigvals_only=True, eigvals=(p - 1, p - 1), check_finite=False)[0]
+ lam)
ridge_obj = lambda x: lr.l2_loss_obj(x, y, X) + lam * lr.l2_reg_obj(x)
ridge_grad = lambda x, XTy, XTX: lr.l2_loss_grad2(
x, XTy, XTX) + lam * lr.l2_reg_grad(x)
if algo == "proj_gd":
x_hat = lib.proj_gd(x,
ridge_grad,
proj.pst_quadrant,
ss,
ridge_obj,
max_iter,
tol,
grad={
"XTX": XTX,
"XTy": XTy
},
proj={})
return x_hat
def linear_svm(y, X, lam, max_iter=1000, tol=1e-7, algo="proj_gd"):
n, p = X.shape
alpha = np.zeros(n)
XTX = np.dot(X.T, X)
XDy = X * y[:, np.newaxis]
ss = lam / max_eigval(
XTX, eigvals_only=True, eigvals=(p - 1, p - 1), check_finite=False)[0]
svm_obj = lambda a: lr.svm_dual_l2_obj(a, XDy, lam)
if algo == "proj_gd":
alpha_hat = lib.proj_gd(alpha,
lr.svm_dual_l2_grad,
proj.interval,
ss,
svm_obj,
max_iter,
tol,
grad={
"XDy": XDy,
"lam": lam
},
proj={
"a": 0.0,
"b": 1.0
})
E = (alpha_hat > 0.0)
return np.dot(XDy[E, :].T, alpha_hat[E]) / lam
def linear_ridge(y, X, lam, max_iter=1000, tol=1e-7, algo="gd"):
n, p = X.shape
x = np.zeros(p)
XTX = np.dot(X.T, X)
XTy = np.dot(X.T, y)
ss = 1.0 / (max_eigval(XTX, eigvals_only=True, eigvals=(p-1, p-1),
check_finite=False)[0] + lam)
ridge_obj = lambda x: lr.l2_loss_obj(x, y, X) + lam * lr.l2_reg_obj(x)
ridge_grad = lambda x, XTy, XTX: lr.l2_loss_grad2(x, XTy, XTX) + lam * lr.l2_reg_grad(x)
if algo == "gd":
x_hat = lib.plain_gd(x, ridge_grad,
ss, ridge_obj, max_iter, tol, XTy=XTy, XTX=XTX )
elif algo == "acc_gd":
x_hat = lib.acc_gd(x, ridge_grad,
ss, ridge_obj, max_iter, tol, XTy=XTy, XTX=XTX )
elif algo == "prox_gd":
x_hat = lib.prox_gd(x, lr.l2_loss_grad2, lr.l2_reg_prox,
ss, lam, ridge_obj, max_iter, tol,
grad={"XTy" : XTy, "XTX" : XTX}, prox={} )
elif algo == "acc_prox_gd":
x_hat = lib.acc_prox_gd(x, lr.l2_loss_grad2, lr.l2_reg_prox,
ss, lam, ridge_obj, max_iter, tol,
grad={"XTy" : XTy, "XTX" : XTX}, prox={} )
elif algo == "acc_gd_restart":
x_hat = lib.acc_gd_restart(x, ridge_grad,
ss, ridge_obj, max_iter, tol, XTy=XTy, XTX=XTX )
elif algo == "acc_prox_gd_restart":
x_hat = lib.acc_prox_gd_restart(x, lr.l2_loss_grad2, lr.l2_reg_prox,
ss, lam, ridge_obj, max_iter, tol,
grad={"XTy" : XTy, "XTX" : XTX}, prox={} )
return x_hat
def linear_slope(y, X, lam, theta, max_iter=1000, tol=1e-7, algo="prox_gd"):
"""
theta in decreasing order
"""
n, p = X.shape
x = np.zeros(p)
XTX = np.dot(X.T, X)
XTy = np.dot(X.T, y)
ss = 1.0 / max_eigval(
XTX, eigvals_only=True, eigvals=(p - 1, p - 1), check_finite=False)[0]
slope_obj = lambda x: lr.l2_loss_obj(x, y, X) + lam * lr.slope_reg_obj(
x, theta)
if algo == "prox_gd":
x_hat = lib.prox_gd(x,
lr.l2_loss_grad2,
lr.slope_reg_prox,
ss,
lam,
slope_obj,
max_iter,
tol,
grad={
"XTy": XTy,
"XTX": XTX
},
prox={"theta": theta})
elif algo == "acc_prox_gd":
x_hat = lib.acc_prox_gd(x,
lr.l2_loss_grad2,
lr.slope_reg_prox,
ss,
lam,
slope_obj,
max_iter,
tol,
grad={
"XTy": XTy,
"XTX": XTX
},
prox={"theta": theta})
elif algo == "acc_prox_gd_restart":
x_hat = lib.acc_prox_gd_restart(x,
lr.l2_loss_grad2,
lr.slope_reg_prox,
ss,
lam,
slope_obj,
max_iter,
tol,
grad={
"XTy": XTy,
"XTX": XTX
},
prox={"theta": theta})
return x_hat
def linear_lasso(y, X, lam, max_iter=1000, tol=1e-7, algo="prox_gd"):
n, p = X.shape
x = np.zeros(p)
XTX = np.dot(X.T, X)
XTy = np.dot(X.T, y)
ss = 1.0 / max_eigval(XTX, eigvals_only=True, eigvals=(p-1, p-1),
check_finite=False)[0]
lasso_obj = lambda x: lr.l2_loss_obj(x, y, X) + lam * lr.l1_reg_obj(x)
if algo == "prox_gd":
x_hat = lib.prox_gd(x, lr.l2_loss_grad2, lr.l1_reg_prox,
ss, lam, lasso_obj, max_iter, tol,
grad={"XTy" : XTy, "XTX" : XTX}, prox={} )
elif algo == "acc_prox_gd":
x_hat = lib.acc_prox_gd(x, lr.l2_loss_grad2, lr.l1_reg_prox,
ss, lam, lasso_obj, max_iter, tol,
grad={"XTy" : XTy, "XTX" : XTX}, prox={} )
return x_hat