선형회귀.md

선형회귀 : 최소제곱법

import tensorflow as tf
import matplotlib.pyplot as plt
import numpy as np

X = [0, 0.5, 1.0, 1.5, 2.0, 2.5]
Y = [0.3, 1.9, 2.4, 4.1, 6.8, 7.9]

x_mean = sum(X)/len(X)
y_mean = sum(Y)/len(Y)

division = sum((y-y_mean)*(x-x_mean) for y, x in list(zip(Y,X)))
divisor = sum((x-x_mean)**2 for x in X)

a = division / divisor
b = y_mean - a * x_mean

new_X = np.arange(0, 3, 0.05)
new_Y = a * new_X + b

print('a:', a, 'b:', b)

plt.plot(X, Y, 'ro', label='Sample Data')
plt.plot(new_X, new_Y, 'b-', label='Test Data')
plt.xlabel('X')
plt.ylabel('Y')
plt.legend()
plt.show()

최소 제곱법은 손실을 구하기 위해 사용한다.

결과물

선형회귀 : 경사하강법

import tensorflow as tf
import matplotlib.pyplot as plt

X = [0, 0.5, 1.0, 1.5, 2.0, 2.5]
Y = [0.3, 1.9, 2.4, 4.1, 6.8, 7.9]

W = tf.Variable(tf.random.uniform([1], -1.0, 1.0))
b = tf.Variable(tf.random.uniform([1], -1.0, 1.0))

optimizer = tf.compat.v1.train.GradientDescentOptimizer(learning_rate=0.1)

@tf.function()
def cost_eval():
  hypothesis = W * X + b
  cost = tf.reduce_mean(tf.square(hypothesis - Y))
  return cost

print("\n  W           b            cost")
for epoch in range(10):
  optimizer.minimize(cost_eval, var_list=[W, b])
  print(epoch, W.numpy(), b.numpy(), cost_eval().numpy())

print("\n=====test=====")
x=5
print("X:", x, "Y:", (W * x + b).numpy())
x=2.5
print("X:", x, "Y:", (W * x + b).numpy())

new_X = tf.range(0, 3, 0.05)
new_Y = W * new_X + b

plt.plot(X, Y, 'ro', label='Sample Data')
plt.plot(new_X, new_Y, 'b-')
plt.xlabel('X')
plt.ylabel('Y')
plt.legend()
plt.show()

결과물