use line function to test linear regression

[crazylk]

use y = 4 + 0.5*x to create test data
but there are no right result.

[trekhleb]

@crazylk could you please share the link to your Jupyter notebook where you're playing with linear regression? I just need to see what training parameters you're using.

[crazylk]

Sorry, I use Java and JavaScript. I don't know python so much and don't know how to use Jupyter, so there are simple python file for you. Maybe there are some mistake. Thank you!

import numpy as np
import random
import matplotlib.pyplot as plt
import pandas as pd
from homemade.linear_regression import LinearRegression

def create_data(in_count):
x_train_list = []
y_train_list = []
x_test_list = []
y_test_list = []
for i in range(0, in_count):
x = 0.0 + i
y = 4 + 0.5 * i
if random.randint(1, 101) > 5:
x_train_list.append(x)
y_train_list.append(y)
else:
x_test_list.append(x)
y_test_list.append(y)

x_train_list = np.array(x_train_list).reshape(len(x_train_list), 1)
y_train_list = np.array(y_train_list).reshape(len(y_train_list), 1)
x_test_list = np.array(x_test_list).reshape(len(x_test_list), 1)
y_test_list = np.array(y_test_list).reshape(len(y_test_list), 1)
return x_train_list, y_train_list, x_test_list, y_test_list

(x_train, y_train, x_test, y_test) = create_data(100)

plt.scatter(x_train, y_train, label='Training Dataset')
plt.scatter(x_test, y_test, label='Test Dataset')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Line function:y = 4 + 0.5*x')
plt.legend()
plt.show()

Set up linear regression parameters.

num_iterations = 50000 # Number of gradient descent iterations.
regularization_param = 0 # Helps to fight model overfitting.
learning_rate = 0.01 # The size of the gradient descent step.
polynomial_degree = 0 # The degree of additional polynomial features.
sinusoid_degree = 0 # The degree of sinusoid parameter multipliers of additional features.

Init linear regression instance.

linear_regression = LinearRegression(x_train, y_train, polynomial_degree, sinusoid_degree)

Train linear regression.

(theta, cost_history) = linear_regression.train(
learning_rate,
regularization_param,
num_iterations
)

Print training results.

print('Initial cost: {:.2f}'.format(cost_history[0]))
print('Optimized cost: {:.2f}'.format(cost_history[-1]))

Print model parameters

theta_table = pd.DataFrame({'Model Parameters': theta.flatten()})
theta_table.head()

Get model predictions for the trainint set.

predictions_num = 1300
x_predictions = np.linspace(x_train.min(), x_train.max(), predictions_num).reshape(predictions_num, 1);
y_predictions = linear_regression.predict(x_predictions)

Plot training data with predictions.

plt.scatter(x_train, y_train, label='Training Dataset')
plt.scatter(x_test, y_test, label='Test Dataset')
plt.plot(x_predictions, y_predictions, 'r', label='Prediction')
plt.xlabel('Economy..GDP.per.Capita.')
plt.ylabel('Happiness.Score')
plt.title('Countries Happines')
plt.legend()
plt.show()

train_cost = linear_regression.get_cost(x_train, y_train, regularization_param)
test_cost = linear_regression.get_cost(x_test, y_test, regularization_param)

print('Train cost: {:.2f}'.format(train_cost))
print('Test cost: {:.2f}'.format(test_cost))

test_predictions = linear_regression.predict(x_test)

test_predictions_table = pd.DataFrame({
'x': x_test.flatten(),
'Test Value': y_test.flatten(),
'Predicted Value': test_predictions.flatten(),
'Prediction Diff': (y_test - test_predictions).flatten()
})

test_predictions_table.head(10)