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linear_regression.py
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linear_regression.py
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from matplotlib import pyplot as plt
import numpy as np
import random
import utils
features = np.array([1, 2, 3, 5, 6, 7])
labels = np.array([155, 197, 244, 356, 407, 448])
print(features)
print(labels)
utils.plot_points(features, labels)
def simple_trick(base_price, price_per_room, num_rooms, price):
small_random_1 = random.random() * 0.1
small_random_2 = random.random() * 0.1
predicted_price = base_price + price_per_room * num_rooms
if price > predicted_price and num_rooms > 0:
price_per_room += small_random_1
base_price += small_random_2
if price > predicted_price and num_rooms < 0:
price_per_room -= small_random_1
base_price += small_random_2
if price < predicted_price and num_rooms > 0:
price_per_room -= small_random_1
base_price -= small_random_2
if price < predicted_price and num_rooms < 0:
price_per_room -= small_random_1
base_price += small_random_2
return price_per_room, base_price
def absolute_trick(base_price, price_per_room, num_rooms, price, learning_rate):
predicted_price = base_price + price_per_room * num_rooms
if price > predicted_price:
price_per_room += learning_rate * num_rooms
base_price += learning_rate
else:
price_per_room -= learning_rate * num_rooms
base_price -= learning_rate
return price_per_room, base_price
def square_trick(base_price, price_per_room, num_rooms, price, learning_rate):
predicted_price = base_price + price_per_room * num_rooms
price_per_room += learning_rate * num_rooms * (price - predicted_price)
base_price += learning_rate * (price - predicted_price)
return price_per_room, base_price
import random
# We set the random seed in order to always get the same results.
random.seed(0)
def linear_regression(features, labels, learning_rate=0.01, epochs=1000):
price_per_room = random.random()
base_price = random.random()
for epoch in range(epochs):
# Uncomment any of the following lines to plot different epochs
# if epoch == 1:
# if epoch <= 10:
# if epoch <= 50:
# if epoch > 50:
if True:
utils.draw_line(price_per_room, base_price, starting=0, ending=8)
i = random.randint(0, len(features) - 1)
num_rooms = features[i]
price = labels[i]
# Uncomment any of the 2 following lines to use a different trick
# price_per_room, base_price = absolute_trick(base_price,
price_per_room, base_price = square_trick(
base_price, price_per_room, num_rooms, price, learning_rate=learning_rate
)
utils.draw_line(price_per_room, base_price, "black", starting=0, ending=8)
utils.plot_points(features, labels)
print("Price per room:", price_per_room)
print("Base price:", base_price)
return price_per_room, base_price
# This line is for the x-axis to appear in the figure
plt.ylim(0, 500)
plt.show()
linear_regression(features, labels, learning_rate=0.01, epochs=1000)
# The root mean square error function
def rmse(labels, predictions):
n = len(labels)
differences = np.subtract(labels, predictions)
return np.sqrt(1.0 / n * (np.dot(differences, differences)))
def linear_regression_with_error_function(features, labels, learning_rate=0.01, epochs=1000):
price_per_room = random.random()
base_price = random.random()
errors = []
for i in range(epochs):
predictions = features[0] * price_per_room + base_price
errors.append(rmse(labels, predictions))
i = random.randint(0, len(features) - 1)
num_rooms = features[i]
price = labels[i]
# Uncomment one of the following 3 lines to use the simple, the absolute, or the square trick
# price_per_room, base_price = simple_trick(base_price,
# price_per_room, base_price = absolute_trick(base_price,
price_per_room, base_price = square_trick(
base_price, price_per_room, num_rooms, price, learning_rate=learning_rate
)
utils.draw_line(price_per_room, base_price, "black", starting=0, ending=9)
utils.plot_points(features, labels)
print("Price per room:", price_per_room)
print("Base price:", base_price)
plt.show()
plt.scatter(range(len(errors)), errors)
plt.show()
return price_per_room, base_price
linear_regression_with_error_function(features, labels, learning_rate=0.01, epochs=1000)