Python 75_ Logistic (sigmoid) 함수

import math

import matplotlib.pyplot as plt

import numpy as np

def odds(p):

    """성공확률 / 실패확률"""

    return p / (1 - p)

def log_odds(p):

    """odds에 log를 취한 값"""

    return math.log(odds(p))

def sigmoid(t):

    """logistic:

    log_odds(odds에 log를 취한 값)을 알고 있을 때, 성공 확률 p를 계산"""

    return 1 / (1 + math.exp(-t))

p = 0.8

print(f'p = {p}, odds(p) = {odds(p)}, log_odds(p) = {log_odds(p)}')

p = 0.8, odds(p) = 4.000000000000001, log_odds(p) = 1.3862943611198908

t = 1.386294361198908

probability = sigmoid(t)

print(f'probability={probability}')

probability=0.8000000000126428

# odds 함수 그래프

xs = np.linspace(0.01, 0.99, 100)

# print(xs)

ys = [odds(x) for x in xs]

plt.plot(xs, ys)

plt.ylim(bottom=0.0, top=10.0)

plt.title('odds')

for i in range(1, 5):

    plt.axhline(y=2 * i, color='0.5')

    plt.axvline(x=0.2 * i, color='0.5')

plt.title('odds')

plt.show()

    

# log_odds 그래프

ys = [log_odds(x) for x in xs]

plt.plot(xs, ys)

plt.axhline(color='0.5')

plt.axvline(color='0.5')

plt.axvline(x=0.5, color='0.5')

plt.axvline(x=1, color='0.5')

plt.title('log_odds')

plt.show()

# logistic ( sigmoid) 함수 그래프

xs = np.linspace(-10, 10, 100)

ys = [sigmoid(x) for x in xs]

plt.plot(xs, ys)

plt.axvline(color='0.5')

plt.axhline( color='0.5')

plt.axhline(y=0.5, color='0.5')

plt.axhline(y=1.0, color='0.5')

plt.title('Logistic(sigmoid)함수')

plt.show()