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paint_regression.py
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paint_regression.py
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import numpy as np
import matplotlib.pyplot as plt
def get_simple_linear_regression_coefficients(x, y):
x = np.array(x)
y = np.array(y)
assert len(x.shape) == 1
assert len(y.shape) == 1
m = len(x)
assert len(y) == m
assert m >= 1
if m == 1:
return y[0], 0.0
mx = np.mean(x)
my = np.mean(y)
sxx = np.sum((x - mx)**2)
sxy = np.sum((x - mx) * (y - my))
beta = sxy / sxx
alpha = my - beta * mx
return alpha, beta
def get_min_sum_squared_residuals(x, y):
# x = np.array(x)
# y = np.array(y)
assert len(x.shape) == 1
assert len(y.shape) == 1
m = len(x)
assert len(y) == m
assert m >= 1
if m == 1:
return 0
mx = np.mean(x)
my = np.mean(y)
sxx = np.sum((x - mx)**2)
syy = np.sum((y - my)**2)
sxy = np.sum((x - mx) * (y - my))
return syy - sxy**2 / sxx
def get_loss(x, y):
x = np.array(x)
y = np.array(y)
assert len(x.shape) == 1
assert len(y.shape) == 1
m = len(x)
assert len(y) == m
assert m >= 1
if m == 1:
return 0
mx = np.mean(x)
my = np.mean(y)
sxx = np.sum((x - mx)**2)
sxy = np.sum((x - mx) * (y - my))
return -sxy**2 / sxx - sxx + 2 * sxy - m * (mx - my)**2
def get_indices_for_paint(x, y):
x = np.array(x)
y = np.array(y)
assert len(x.shape) == 1
assert len(y.shape) == 1
m = len(x)
assert len(y) == m
min_L = np.inf
best_indices = None
for size in range(1, m + 1):
for min_i in range(m - size + 1):
x_in = x[min_i : min_i + size]
y_in = y[min_i : min_i + size]
# x_out = np.concatenate((x[:min_i], x[min_i + size:]))
# y_out = np.concatenate((y[:min_i], y[min_i + size:]))
# L_in = get_min_sum_squared_residuals(x_in, y_in)
# L_out = np.sum((x_out - y_out)**2)
# L = L_in + L_out
L = get_loss(x_in, y_in)
if L < min_L:
best_indices = np.arange(min_i, min_i + size)
min_L = L
return best_indices, min_L
def main():
# x = np.array([1.0, 2, 3, 7, 12])
# y = np.array([4.0, 5, 10, 3, 13])
# print(x)
# for _ in range(3):
# best_indices, L = get_indices_for_paint(x, y)
# alpha, beta = get_simple_linear_regression_coefficients(x[best_indices], y[best_indices])
# x[best_indices] = alpha + beta * x[best_indices]
# print(best_indices, L)
# print(x)
# best_indices, L = get_indices_for_paint(x, y)
# print(best_indices)
# print(get_loss(x[:1], y[:1]))
# print(get_loss(x[1:], y[1:]))
m = 100
x = np.random.randn(m)
y = np.random.randn(m)
for _ in range(10):
best_indices, L = get_indices_for_paint(x, y)
print(best_indices)
print(np.sum((x - y)**2), L)
alpha, beta = get_simple_linear_regression_coefficients(x[best_indices], y[best_indices])
x[best_indices] = alpha + beta * x[best_indices]
# print(x)
losses = np.zeros((m, m))
for size in range(1, m + 1):
for min_i in range(m - size + 1):
x_in = x[min_i : min_i + size]
y_in = y[min_i : min_i + size]
L = get_loss(x_in, y_in)
losses[min_i, min_i + size - 1] = L
plt.matshow(losses)
plt.show()
plt.scatter(x, y)
plt.show()
# print(get_loss(x[:100], y[:100]))
# print(get_loss(x[100:], y[100:]))
print(get_loss(x[:50], y[:50]) + get_loss(x[50:], y[50:]))
print(get_loss(x, y))
if __name__ == '__main__':
main()
'''
-sxy**2 / sxx - sxx + 2 * sxy - m * (mx - my)**2
sxy**2 / sxx - 2 * sxy + sxx + m * (mx - my)**2
sxy**2 / sxx - 2 * sxy + sxx + m * (mx - my)**2
'''