def first_principal_component_sgd(X):
guess = [1 for _ in X[0]]
unscaled_maximizer = maximize_stochastic(
lambda x, _, w: directional_variance_i(x, w),
lambda x, _, w: directional_variance_gradient_i(x, w),
X, [None for _ in X], guess)
return direction(unscaled_maximizer)
def first_principal_component_stochastic(matrix):
guess = [1 for _ in matrix[0]]
unscaled_maximizer = maximize_stochastic(
lambda x, _, vector: directional_variance_row(x, vector),
lambda x, _, vector: directional_variance_gradient_row(x, vector),
matrix,
[None for _ in matrix[0]], # fake "y"
guess)
return direction(unscaled_maximizer)
def first_principal_component_stochastic(matrix):
guess = [1 for _ in matrix[0]]
unscaled_maximizer = maximize_stochastic(
lambda x, _, vector: directional_variance_row(x, vector),
lambda x, _, vector: directional_variance_gradient_row(x, vector),
matrix,
[None for _ in matrix[0]], # fake "y"
guess
)
return direction(unscaled_maximizer)
# want to maximize log likelihood on the training data
fn = partial(logistic_log_likelihood, x_train, y_train)
gradient_fn = partial(logistic_log_gradient, x_train, y_train)
# pick a random starting point
beta_0 = [1, 1, 1]
# and maximize using gradient descent
beta_hat = maximize_batch(fn, gradient_fn, beta_0)
print "beta_batch", beta_hat
beta_0 = [1, 1, 1]
beta_hat = maximize_stochastic(logistic_log_likelihood_i,
logistic_log_gradient_i, x_train, y_train,
beta_0)
print "beta stochastic", beta_hat
true_positives = false_positives = true_negatives = false_negatives = 0
for x_i, y_i in zip(x_test, y_test):
predict = logistic(dot(beta_hat, x_i))
if y_i == 1 and predict >= 0.5: # TP: paid and we predict paid
true_positives += 1
elif y_i == 1: # FN: paid and we predict unpaid
false_negatives += 1
elif predict >= 0.5: # FP: unpaid and we predict paid
false_positives += 1
# want to maximize log likelihood on the training data
fn = partial(logistic_log_likelihood, x_train, y_train)
gradient_fn = partial(logistic_log_gradient, x_train, y_train)
# pick a random starting point
beta_0 = [1, 1, 1]
# and maximize using gradient descent
beta_hat = maximize_batch(fn, gradient_fn, beta_0)
print("beta_batch", beta_hat)
beta_0 = [1, 1, 1]
beta_hat = maximize_stochastic(logistic_log_likelihood_i,
logistic_log_gradient_i,
x_train, y_train, beta_0)
print("beta stochastic", beta_hat)
true_positives = false_positives = true_negatives = false_negatives = 0
for x_i, y_i in zip(x_test, y_test):
predict = logistic(dot(beta_hat, x_i))
if y_i == 1 and predict >= 0.5: # TP: paid and we predict paid
true_positives += 1
elif y_i == 1: # FN: paid and we predict unpaid
false_negatives += 1
elif predict >= 0.5: # FP: unpaid and we predict paid
false_positives += 1