Regression

regression.py

import matplotlib.pyplot as plt
import numpy as np


def generate_points(a, b, number_points=500):
    x_points = np.random.normal(0, np.random.randint(0, number_points / 10), number_points)
    y_points = (a * x_points + b) + np.random.normal(0, number_points / 2, number_points)
    return np.array(x_points, dtype=float), np.array(y_points, dtype=float)


def linear_regression_analytical(x, y, plot=False):
    n = len(x)
    numer = n * sum(x * y) - sum(x) * sum(y)
    denom = n * sum(x ** 2) - sum(x) ** 2

    a = numer / denom
    b = sum(y) / n - a * (sum(x) / n)

    print("y = " + str(a) + "x + " + str(b))

    if plot:
        plt.scatter(x, y)
        plt.plot(x, a * x + b, color="green")
        plt.savefig("analytical.png")
        plt.show()

    return a, b


def gradient_descent(start_a, start_b, x, y, iterations, step, plot=False):
    number_points = len(x)
    result_a, result_b = start_a, start_b

    for i in range(iterations):

        if i % 500 == 0 and plot:
            plt.plot(x, result_a * x + result_a, color="red")

        a_gradient = sum(-(2 / number_points) * x * (y - (result_a * x + result_b)))
        b_gradient = sum(-(2 / number_points) * (y - (result_a * x + result_b)))
        result_a = result_a - (step * a_gradient)
        result_b = result_b - (step * b_gradient)

    print("Gradient descent => y = " + str(result_a) + "x + " + str(result_b))

    if plot:
        plt.scatter(x, y)
        plt.plot(x, result_a * x + result_a, color="green")
        plt.savefig("gradient_descent.png")
        plt.show()


def test_linreg():
    a = 2.5
    b = 1.4
    points = generate_points(a, b, 100)

    print("Original a:", a, "b:", b)
    plt.plot(points[0], a * points[0] + b, color="red")
    print("Calculated a,b:", linear_regression_analytical(points[0], points[1], plot=True))


def load_file(name):
    file = open(name)
    read_file = file.read()
    lines = read_file.split("\n")
    x = []
    y = []
    for line in lines:
        xy = line.split(" ")
        x.append(float(xy[0]))
        y.append(float(xy[1]))

    return np.array(x, dtype=float), np.array(y, dtype=float)


# x, y = load_file("exfiles/oldfailthful.txt")
# #linear_regression_analytical(x, y, True)
#
# a = 2.5
# b = 1.4
# o, p = generate_points(a, b, 100)
#
# gradient_descent(5, 0.5, o, p, 6000, 0.0001, plot=True)
#
# #test_linreg()