def predict(x_i, beta):
return dot(x_i, beta)
def ridge_penalty(beta, alpha):
return alpha * dot(beta[1:], beta[1:])
def predict(x_i, beta):
return dot(x_i, beta)
print()
random.seed(0) # so that you get the same results as me
bootstrap_betas = bootstrap_statistic(list(zip(x, daily_minutes_good)),
estimate_sample_beta, 100)
bootstrap_standard_errors = [
standard_deviation([beta[i] for beta in bootstrap_betas])
for i in range(4)
]
print("bootstrap standard errors", bootstrap_standard_errors)
print()
print("p_value(30.63, 1.174)", p_value(30.63, 1.174))
print("p_value(0.972, 0.079)", p_value(0.972, 0.079))
print("p_value(-1.868, 0.131)", p_value(-1.868, 0.131))
print("p_value(0.911, 0.990)", p_value(0.911, 0.990))
print()
print("regularization")
random.seed(0)
for alpha in [0.0, 0.01, 0.1, 1, 10]:
beta = estimate_beta_ridge(x, daily_minutes_good, alpha=alpha)
print("alpha", alpha)
print("beta", beta)
print("dot(beta[1:],beta[1:])", dot(beta[1:], beta[1:]))
print("r-squared", multiple_r_squared(x, daily_minutes_good, beta))
print()
def ridge_penalty(beta, alpha): return alpha * dot(beta[1:], beta[1:])
print()
random.seed(0) # so that you get the same results as me
bootstrap_betas = bootstrap_statistic(list(zip(x, daily_minutes_good)),
estimate_sample_beta,
100)
bootstrap_standard_errors = [
standard_deviation([beta[i] for beta in bootstrap_betas])
for i in range(4)]
print("bootstrap standard errors", bootstrap_standard_errors)
print()
print("p_value(30.63, 1.174)", p_value(30.63, 1.174))
print("p_value(0.972, 0.079)", p_value(0.972, 0.079))
print("p_value(-1.868, 0.131)", p_value(-1.868, 0.131))
print("p_value(0.911, 0.990)", p_value(0.911, 0.990))
print()
print("regularization")
random.seed(0)
for alpha in [0.0, 0.01, 0.1, 1, 10]:
beta = estimate_beta_ridge(x, daily_minutes_good, alpha=alpha)
print("alpha", alpha)
print("beta", beta)
print("dot(beta[1:],beta[1:])", dot(beta[1:], beta[1:]))
print("r-squared", multiple_r_squared(x, daily_minutes_good, beta))
print()
def logistic_log_partial_ij(x_i, y_i, beta, j):
"""here i is the index of the data point,
j the index of the derivative"""
return (y_i - logistic(dot(x_i, beta))) * x_i[j]
def logistic_log_likelihood_i(x_i, y_i, beta):
if y_i == 1:
return np.log(logistic(dot(x_i, beta)))
else:
return np.log(1 - logistic(dot(x_i, beta)))
print("\nlogistic regression:")
random.seed(0)
x_train, x_test, y_train, y_test = train_test_split(rescaled_x, y, 0.1)
beta_0 = [random.random() for _ in range(3)]
beta_hat = maximize_stochastic(logistic_log_likelihood_i,
logistic_log_gradient_i,
x_train, y_train, beta_0)
print("Beta Stochastic Gradient Value : ", 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
else: # TN: unpaid and we predict unpaid
true_negatives += 1
precision = true_positives / (true_positives + false_positives) # Given a positive output from the LR, what is the probability that it is correct?
recall = true_positives / (true_positives + false_negatives) # Given a positive sample, will LR correctly identify it as Positive.
print("True Positive : ", true_positives, " False Positive : ", false_positives, " True Negative : ", true_negatives, " False Negative : ", false_negatives)
