A simple Regression AI

regress.py

from collections import namedtuple

Point = namedtuple("Point", ["x", "y"]) # Point(1, 2).x == 1 and Point(1, 2).y == 2
mean = lambda values: sum(values) / len(values)

class Regression(object):
    def __init__(self, points):
        self.slope = 0 # we'll use gradient descent to find this
        self.point = Point(0, 0) # we'll use that stat fact to recalculate this
        self.learn_from_data_set(points)

    def __str__(self):
        return "Regression with slope " + str(self.slope) + " and point " + str(self.point)

    # make it possible to write Regression[x] to calculate the value at x
    def __getitem__(self, x):
        return self.slope * (x - self.point.x) + self.point.y

    # total inaccuracy
    def cost(self, data_points):
        return sum((self[point.x] - point.y) ** 2 for point in data_points)

    def derivative_of_cost_with_respect_to_slope(self, data_points):
        infinitesimal = 10 ** -5

        original_cost = self.cost(data_points)
        self.slope += infinitesimal
        new_cost = self.cost(data_points)
        self.slope -= infinitesimal

        return (new_cost - original_cost) / infinitesimal

    def learn_from_data_set(self, data_points):
        # (average x, average y) MUST be on the regression
        mean_x = mean([point.x for point in data_points])
        mean_y = mean([point.y for point in data_points])
        self.point = Point(mean_x, mean_y)

        # use gradient descent to find slope
        eta = 0.0001
        while abs(self.derivative_of_cost_with_respect_to_slope(data_points)) > 0.000001:
            self.slope -= eta * self.derivative_of_cost_with_respect_to_slope(data_points)

# demo
print Regression([
    Point(30., 66.),
    Point(34., 79.),
    Point(27., 70.),
    Point(25., 60.),
    Point(17., 48.),
    Point(23., 55.),
    Point(20., 60.)
])