def least_squares(y, tx):
"""Least squares optimisation. Returns the optimal weights vector"""
from helpers_optimization import compute_loss
weights = np.linalg.solve(tx.T.dot(tx), tx.T.dot(y))
loss = compute_loss(y, tx, weights, 'rmse')
return weights, loss
def ridge_regression(y, tx, lambda_):
"""Least squares with regularisation. Returns optimal weight vector"""
from helpers_optimization import compute_loss
aI = 2 * tx.shape[0] * lambda_ * np.identity(tx.shape[1])
weights = np.linalg.solve(tx.T.dot(tx) + aI, tx.T.dot(y))
loss = compute_loss(y, tx, weights, 'rmse')
return weights, loss
def logistic_regression(y, tx, initial_w, max_iters, gamma):
"""Logistic regression with Gradient descent algorithm. Returns the updated weights and the loss value for this set of weights"""
from helpers_optimization import compute_logistic_gradient, compute_loss
w = initial_w
for n_iter in range(max_iters):
# compute loss, gradient
grad = compute_logistic_gradient(y, tx, w)
# gradient w by descent update
w = w - gamma * grad
print("Logistic regression: w={}".format(w))
loss = compute_loss(y, tx, w, 'logl')
return w, loss
def reg_logistic_regression(y, tx, lambda_, initial_w, max_iters, gamma):
"""Regularized logistic regression with Gradient descent algorithm. Returns the updated weights and the loss value for this set of weights"""
from helpers_optimization import compute_logistic_gradient, compute_loss
w = initial_w
for n_iter in range(max_iters):
#loss = compute_logistic_loss(y, tx, w) + lambda_ * np.squeeze(w.T.dot(w))
gradient = compute_logistic_gradient(y, tx, w) + 2 * lambda_ * w
w -= gamma * gradient
print(
"Regularized logistic regression (lambda = {lamb},{ti}) : w={weights}".
format(lamb=lambda_, ti=max_iters - 1, weights=w))
loss = compute_loss(y, tx, w, 'logl_r')
return w, loss
def least_squares_GD(y, tx, initial_w, max_iters, gamma):
"""Least square Gradient descent algorithm. Returns the updated weights and the loss value for this set of weights"""
from helpers_optimization import compute_gradient, compute_loss
w = initial_w
for n_iter in range(max_iters):
# compute loss, gradient
grad, _ = compute_gradient(y, tx, w)
# gradient w by descent update
w = w - gamma * grad
print("Gradient Descent (gamma = {gamma} ,{ti}): w ={weights}".format(
gamma=gamma, ti=max_iters - 1, weights=w))
loss = compute_loss(y, tx, w, 'rmse')
return w, loss
def least_squares_SGD(y, tx, initial_w, max_iters, gamma, batchsize):
"""Stochastic gradient descent. Returns the updated weights and the loss value for this set of weights"""
from helpers_data import batch_iter
from helpers_optimization import compute_gradient, compute_loss
weights = initial_w
for n_iter in range(max_iters): # iterations
for batch in range(batchsize): # for different batchsize
for y_batch, tx_batch in batch_iter(y,
tx,
batch_size=batch,
num_batches=1):
# compute a stochastic gradient and loss
grad, _ = compute_gradient(y_batch, tx_batch, w)
# update w through the stochastic gradient update
weights = w - gamma * grad
print("SGD(gamma = {gamma},{ti}): w={weight}".format(gamma=gamma,
ti=max_iters - 1,
weight=weights))
loss = compute_loss(y, tx, weights, 'rmse')
return weights, loss