31 KiB
31 KiB
Część podstawowa
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
data = pd.read_csv('fires_thefts.csv', names = ['fires', 'thefts'])
x = data[['fires']].to_numpy().flatten()
y = data[['thefts']].to_numpy().flatten()
def gradient_descent(h, cost_fun, theta, x, y, alpha, eps, max_steps = 1000000):
current_cost = cost_fun(h, theta, x, y)
log = [[current_cost, theta]]
m = len(y)
steps_counter = 0
while True and steps_counter < max_steps:
steps_counter += 1
new_theta = [
theta[0] - alpha/float(m) * sum(h(theta, x[i]) - y[i]
for i in range(m)),
theta[1] - alpha/float(m) * sum((h(theta, x[i]) - y[i]) * x[i]
for i in range(m))]
theta = new_theta
prev_cost = current_cost
current_cost = cost_fun(h, theta, x, y)
if abs(prev_cost - current_cost) <= eps:
break
log.append([current_cost, theta])
return theta, log
def J(h, theta, x, y):
m = len(y)
return 1.0 / (2 * m) * sum((h(theta, x[i]) - y[i])**2 for i in range(m))
def h(theta, x):
return theta[0] + theta[1] * x
def mse(expected, predicted):
m = len(expected)
if len(predicted) != m:
raise Exception('Wektory mają różne długości!')
return 1.0 / (2 * m) * sum((expected[i] - predicted[i])**2 for i in range(m))
best_theta, log = gradient_descent(h, J, [0.0, 0.0], x, y, alpha=0.001, eps=0.0000001, max_steps = 1000000)
predicted_50 = h(best_theta, 50)
predicted_100 = h(best_theta, 100)
predicted_200 = h(best_theta, 200)
print(f'Predicted amount of thefts for 50 fires: {predicted_50}')
print(f'Predicted amount of thefts for 100 fires: {predicted_100}')
print(f'Predicted amount of thefts for 200 fires: {predicted_200}')Predicted amount of thefts for 50 fires: 82.70999487819813 Predicted amount of thefts for 100 fires: 148.45251499453076 Predicted amount of thefts for 200 fires: 279.93755522719596
Część zaawansowana
best_theta_01, log_01 = gradient_descent(h, J, [0.0, 0.0], x, y, alpha = 0.1, eps = 0.0000001, max_steps = 1000)
best_theta_001, log_001 = gradient_descent(h, J, [0.0, 0.0], x, y, alpha = 0.01, eps = 0.0000001, max_steps = 1000)
best_theta_0001, log_0001 = gradient_descent(h, J, [0.0, 0.0], x, y, alpha = 0.001, eps = 0.0000001, max_steps = 1000)
steps_range = np.arange(0, 200, 1)
y_01, y_001, y_0001 = [], [], []
for step in steps_range:
y_01.append(log_01[step][0])
y_001.append(log_001[step][0])
y_0001.append(log_0001[step][0])
fig = plt.figure(figsize=(8, 7))
ax = fig.add_subplot(111)
ax.plot(steps_range, y_01, label='alpha = 0.1')
ax.plot(steps_range, y_001, label='alpha = 0.01')
ax.plot(steps_range, y_0001, label='alpha = 0.001')
ax.legend(loc='best')
ax.set_xlabel('krok')
ax.set_ylabel(r'$J(\theta)$')
# plt.ylim([0, 800])
plt.show()/var/folders/lm/cbc3n48n4x94zd3vf6zbbly40000gn/T/ipykernel_46784/756364182.py:32: RuntimeWarning: overflow encountered in scalar power return 1.0 / (2 * m) * sum((h(theta, x[i]) - y[i])**2 for i in range(m)) /var/folders/lm/cbc3n48n4x94zd3vf6zbbly40000gn/T/ipykernel_46784/756364182.py:25: RuntimeWarning: invalid value encountered in scalar subtract if abs(prev_cost - current_cost) <= eps: /var/folders/lm/cbc3n48n4x94zd3vf6zbbly40000gn/T/ipykernel_46784/756364182.py:20: RuntimeWarning: overflow encountered in scalar add theta[1] - alpha/float(m) * sum((h(theta, x[i]) - y[i]) * x[i] /var/folders/lm/cbc3n48n4x94zd3vf6zbbly40000gn/T/ipykernel_46784/756364182.py:20: RuntimeWarning: overflow encountered in scalar multiply theta[1] - alpha/float(m) * sum((h(theta, x[i]) - y[i]) * x[i] /var/folders/lm/cbc3n48n4x94zd3vf6zbbly40000gn/T/ipykernel_46784/756364182.py:20: RuntimeWarning: invalid value encountered in scalar subtract theta[1] - alpha/float(m) * sum((h(theta, x[i]) - y[i]) * x[i] /var/folders/lm/cbc3n48n4x94zd3vf6zbbly40000gn/T/ipykernel_46784/756364182.py:32: RuntimeWarning: overflow encountered in scalar add return 1.0 / (2 * m) * sum((h(theta, x[i]) - y[i])**2 for i in range(m))