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logistic_regression.py
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import math
import random
import matplotlib.pyplot as plt
from linear_algebra import dot, vector_add
from multiple_regression import estimate_beta, predict
from working_with_data import rescale
from functools import reduce, partial
from machine_learning import train_test_split
from gradient_descent import maximize_batch
def logistic(x):
return 1.0 / (1 + math.exp(-x))
def logistic_prime(x):
return logistic(x) * (1 - logistic(x))
def logistic_log_likelihood(x, y, beta):
return sum(logistic_log_likekihood_i(x_i, y_i, beta)
for x_i, y_i in zip(x, y))
def logistic_log_likekihood_i(x_i, y_i, beta):
if y_i == 1:
return math.log(logistic(dot(x_i, beta)))
else:
return math.log(1 - logistic(dot(x_i, beta)))
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_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_graident_i(x_i, y_i, beta):
"""the gradient of the log likelihood
corresponding to the ith data point"""
return [logistic_log_partial_ij(x_i, y_i, beta, j)
for j, _ in enumerate(beta)]
def logistic_log_gradient(x, y, beta):
return reduce(vector_add,
[logistic_log_graident_i(x_i, y_i, beta)
for x_i, y_i in zip(x,y)])
data = [(0.7, 48000, 1), (1.9, 48000, 0), (2.5, 60000, 1), (4.2, 63000, 0), (6, 76000, 0), (6.5, 69000, 0),
(7.5, 76000, 0), (8.1, 88000, 0), (8.7, 83000, 1), (10, 83000, 1), (0.8, 43000, 0), (1.8, 60000, 0),
(10, 79000, 1), (6.1, 76000, 0), (1.4, 50000, 0), (9.1, 92000, 0), (5.8, 75000, 0), (5.2, 69000, 0),
(1, 56000, 0), (6, 67000, 0), (4.9, 74000, 0), (6.4, 63000, 1), (6.2, 82000, 0), (3.3, 58000, 0),
(9.3, 90000, 1), (5.5, 57000, 1), (9.1, 102000, 0), (2.4, 54000, 0), (8.2, 65000, 1), (5.3, 82000, 0),
(9.8, 107000, 0), (1.8, 64000, 0), (0.6, 46000, 1), (0.8, 48000, 0), (8.6, 84000, 1), (0.6, 45000, 0),
(0.5, 30000, 1), (7.3, 89000, 0), (2.5, 48000, 1), (5.6, 76000, 0), (7.4, 77000, 0), (2.7, 56000, 0),
(0.7, 48000, 0), (1.2, 42000, 0), (0.2, 32000, 1), (4.7, 56000, 1), (2.8, 44000, 1), (7.6, 78000, 0),
(1.1, 63000, 0), (8, 79000, 1), (2.7, 56000, 0), (6, 52000, 1), (4.6, 56000, 0), (2.5, 51000, 0),
(5.7, 71000, 0), (2.9, 65000, 0), (1.1, 33000, 1), (3, 62000, 0), (4, 71000, 0), (2.4, 61000, 0),
(7.5, 75000, 0), (9.7, 81000, 1), (3.2, 62000, 0), (7.9, 88000, 0), (4.7, 44000, 1), (2.5, 55000, 0),
(1.6, 41000, 0), (6.7, 64000, 1), (6.9, 66000, 1), (7.9, 78000, 1), (8.1, 102000, 0), (5.3, 48000, 1),
(8.5, 66000, 1), (0.2, 56000, 0), (6, 69000, 0), (7.5, 77000, 0), (8, 86000, 0), (4.4, 68000, 0),
(4.9, 75000, 0), (1.5, 60000, 0), (2.2, 50000, 0), (3.4, 49000, 1), (4.2, 70000, 0), (7.7, 98000, 0),
(8.2, 85000, 0), (5.4, 88000, 0), (0.1, 46000, 0), (1.5, 37000, 0), (6.3, 86000, 0), (3.7, 57000, 0),
(8.4, 85000, 0), (2, 42000, 0), (5.8, 69000, 1), (2.7, 64000, 0), (3.1, 63000, 0), (1.9, 48000, 0),
(10, 72000, 1), (0.2, 45000, 0), (8.6, 95000, 0), (1.5, 64000, 0), (9.8, 95000, 0), (5.3, 65000, 0),
(7.5, 80000, 0), (9.9, 91000, 0), (9.7, 50000, 1), (2.8, 68000, 0), (3.6, 58000, 0), (3.9, 74000, 0),
(4.4, 76000, 0), (2.5, 49000, 0), (7.2, 81000, 0), (5.2, 60000, 1), (2.4, 62000, 0), (8.9, 94000, 0),
(2.4, 63000, 0), (6.8, 69000, 1), (6.5, 77000, 0), (7, 86000, 0), (9.4, 94000, 0), (7.8, 72000, 1),
(0.2, 53000, 0), (10, 97000, 0), (5.5, 65000, 0), (7.7, 71000, 1), (8.1, 66000, 1), (9.8, 91000, 0),
(8, 84000, 0), (2.7, 55000, 0), (2.8, 62000, 0), (9.4, 79000, 0), (2.5, 57000, 0), (7.4, 70000, 1),
(2.1, 47000, 0), (5.3, 62000, 1), (6.3, 79000, 0), (6.8, 58000, 1), (5.7, 80000, 0), (2.2, 61000, 0),
(4.8, 62000, 0), (3.7, 64000, 0), (4.1, 85000, 0), (2.3, 51000, 0), (3.5, 58000, 0), (0.9, 43000, 0),
(0.9, 54000, 0), (4.5, 74000, 0), (6.5, 55000, 1), (4.1, 41000, 1), (7.1, 73000, 0), (1.1, 66000, 0),
(9.1, 81000, 1), (8, 69000, 1), (7.3, 72000, 1), (3.3, 50000, 0), (3.9, 58000, 0), (2.6, 49000, 0),
(1.6, 78000, 0), (0.7, 56000, 0), (2.1, 36000, 1), (7.5, 90000, 0), (4.8, 59000, 1), (8.9, 95000, 0),
(6.2, 72000, 0), (6.3, 63000, 0), (9.1, 100000, 0), (7.3, 61000, 1), (5.6, 74000, 0), (0.5, 66000, 0),
(1.1, 59000, 0), (5.1, 61000, 0), (6.2, 70000, 0), (6.6, 56000, 1), (6.3, 76000, 0), (6.5, 78000, 0),
(5.1, 59000, 0), (9.5, 74000, 1), (4.5, 64000, 0), (2, 54000, 0), (1, 52000, 0), (4, 69000, 0), (6.5, 76000, 0),
(3, 60000, 0), (4.5, 63000, 0), (7.8, 70000, 0), (3.9, 60000, 1), (0.8, 51000, 0), (4.2, 78000, 0),
(1.1, 54000, 0), (6.2, 60000, 0), (2.9, 59000, 0), (2.1, 52000, 0), (8.2, 87000, 0), (4.8, 73000, 0),
(2.2, 42000, 1), (9.1, 98000, 0), (6.5, 84000, 0), (6.9, 73000, 0), (5.1, 72000, 0), (9.1, 69000, 1),
(9.8, 79000, 1), ]
data = list(map(list, data)) # change tuples to lists
x = [[1] + row[:2] for row in data]
y = [row[2] for row in data]
rescaled_x = rescale(x)
beta = estimate_beta(rescaled_x, y)
print(beta)
predictions = [predict(x_i, beta) for x_i in rescaled_x]
print(predictions)
#plt.scatter(predictions, y)
#plt.xlabel("predicted")
#plt.ylabel("actual")
#plt.show()
random.seed(0)
x_train, x_test, y_train, y_test = train_test_split(rescaled_x, y, 0.33)
# want to maximixe 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)
beta_0 = [random.random() for _ in range(3)]
beta_hat = maximize_batch(fn, gradient_fn, beta_0)
print(beta_hat)
true_positive = false_positive = true_negative = false_negative = 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:
true_positive += 1
elif y_i == 1:
false_negative += 1
elif predict >= 0.5:
false_positive += 1
else:
true_negative += 1
precision = true_positive / (true_positive + false_positive)
recall = true_positive / (true_positive + false_negative)
print(precision)
print(recall)
predictions = [logistic(dot(beta_hat, x_i)) for x_i in x_test]
plt.scatter(predictions, y_test)
plt.xlabel("Predicted Probability")
plt.ylabel("Acutal Outcome")
plt.title("Logistic Regression Predicted vs. Acutal")
plt.show()