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old_functions.py
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Mon, Feb 24, 02:10

old_functions.py
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import datetime
import numpy as np
import matplotlib.pyplot as plt
from proj1_helpers import *
def compute_mse(y, tx, w):
return np.mean((y-tx@w)**2)/2
def least_squares(y, tx):
"""calculate the least squares solution."""
X = np.transpose(tx)@tx
Y = np.transpose(tx)@y
w = np.linalg.pinv(X)@Y
mse = np.mean((y-tx@w)**2)/2
return mse, w
def compute_mse_gradient(y, tx, w):
"""Compute the gradient."""
gradient_helper = np.transpose([(y-tx@w)]*np.shape(tx)[1])
return np.sum(gradient_helper*(-tx),axis=0)/len(y)
def least_squares_GD(y, tx, initial_w, max_iters, gamma):
"""Gradient descent algorithm."""
# Define parameters to store w and loss
ws = [initial_w]
losses = []
w = initial_w
for n_iter in range(max_iters):
# ***************************************************
gradient = compute_mse_gradient(y,tx,w)
loss = compute_mse(y,tx,w)
# ***************************************************
w = w - gamma*gradient
# ***************************************************
ws.append(w)
losses.append(loss)
print("Gradient Descent({bi}/{ti}): loss={l}, w0={w0}, w1={w1}".format(
bi=n_iter, ti=max_iters - 1, l=loss, w0=w[0], w1=w[1]))
return losses, ws
def least_squares_SGD(y, tx, initial_w, batch_size, max_iters, gamma):
"""Stochastic gradient descent algorithm."""
# ***************************************************
ws = [initial_w]
losses = []
w = initial_w
for n_iter in range(max_iters):
for y_i,tx_i in batch_iter(y,tx,batch_size):
gradient = compute_mse_gradient(y_i,tx_i,w)
loss = compute_mse(y_i,tx_i,w)
w = w - gamma*gradient
ws.append(w)
losses.append(loss)
print("Stochastic Gradient Descent({bi}/{ti}): loss={l}, w0={w0}, w1={w1}".format(
bi=n_iter, ti=max_iters - 1, l=loss, w0=w[0], w1=w[1]))
return losses, ws
def ridge_regression(y, tx, lambda_):
"""implement ridge regression."""
L = np.identity(tx.shape[1])
#L[0][0] = 0
a = np.transpose(tx)@tx + 2*len(y)*lambda_*L
b = np.transpose(tx)@y
w = np.linalg.solve(a,b)
return compute_mse(y,tx,w),w
def sigmoid(t):
return 1/(1+np.power(np.e,-t))
def calculate_log_loss(y, tx, w):
"""compute the cost by negative log likelihood."""
return np.sum(np.log(1 + np.power(np.e,tx@w)) - y*tx@w)
def calculate_log_gradient(y, tx, w):
"""compute the gradient of loss."""
return tx.T@(sigmoid(tx@w)-y)
def calculate_hessian(y, tx, w):
"""return the hessian of the loss function."""
S = sigmoid(tx@w)*(1-sigmoid(tx@w))
S = np.identity(len(S))*S
return (tx.T@S@tx)
def logistic_gradient_descent(y, tx, w, gamma):
"""
Do one step of gradient descen using logistic regression.
Return the loss and the updated w.
"""
# ***************************************************
loss = calculate_log_loss(y,tx,w)
# ***************************************************
gradient = calculate_log_gradient(y,tx,w)
# ***************************************************
w = w - gamma*gradient
# ***************************************************
return loss, w
def logistic_regression(y, tx, w):
"""return the loss, gradient, and hessian."""
loss = calculate_log_loss(y,tx,w)
gradient = calculate_log_gradient(y,tx,w)
hessian = calculate_hessian(y,tx,w)
return loss, gradient, hessian
def learning_by_newton_method(y, tx, w):
"""
Do one step on Newton's method.
return the loss and updated w.
"""
loss,gradient,hessian = logistic_regression(y,tx,w)
# ***************************************************
w_new = w-np.linalg.pinv(hessian)@gradient
return loss, w_new
def penalized_logistic_regression(y, tx, w, lambda_):
"""return the loss, gradient, and hessian."""
loss = np.sum(np.log(1 + np.exp(tx@w)) - y*tx@w)
gradient = tx.T@(sigmoid(tx@w) - y) + lambda_*w
hessian = calculate_hessian(y,tx,w) + lambda_*np.identity(len(w))
return loss,gradient,hessian
def learning_by_penalized_gradient(y, tx, w, gamma, lambda_):
loss,gradient,hessian = penalized_logistic_regression(y,tx,w,lambda_)
# ***************************************************
w_new = w-np.linalg.pinv(hessian)@gradient #w-gamma*gradient
return loss, w_new

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