경사 하강법(Gradient Descent)

경사하강법

1.Machine( ) 정의

import numpy as np

def Machine(x, w, b):
    y_hat = (w * x) + b
    return y_hat

x = np.array([1, 3, 5, 7, 9])
w = 2
b = 1

#x, w, b 객체 지정

Machine(x, w, b)

array([ 3, 7, 11, 15, 19])

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2.Gradient( ) 정의

def Gradient(x, y, w, b):
    y_hat = Machine(x, w, b)

    dw = np.mean((y - y_hat) * (-2 * x))
    db = np.mean((y - y_hat) * (-2))

    return dw, db

y = np.array([2, 4, 6, 8, 10])

dw, db = Gradient(x, y, w, b)

print('dw is ', dw)
print('db is ', db)

dw is 66.0 db is 10.0

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3.Learning( ) 정의

def Learning(x, y, w, b, step):
    dw, db = Gradient(x, y, w, b)
    
    uw = w - step * dw
    ub = b - step * db
    
    return uw, ub

step = 0.05

uw, ub = Learning(x, y, w, b, step)

print('Updated_w is ', '%.3f' % uw)
print('Updated_b is ', '%.3f' % ub)

Updated_w is -1.300

Updated_b is 0.500

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4.testData.csv에 적용

import pandas as pd
import matplotlib.pyplot as plt

DATA = pd.read_csv

DATA.info()

DATA.head()

plt.scatter(DATA.inputs, DATA.outputs, s = 0.5)
plt.show()

w = 2
b = 3
step = 0.05 

for i in range(0, 1500):  #1500번 학습
    uw, ub = Learning(DATA.inputs, DATA.outputs, w, b, step)
    w = uw
    b = ub

print('Learned_w is ', '%.3f' % w)
print('Learned_b is ', '%.3f' % b)

Learned_w is 0.505

Learned_b is -0.170

# 학습결과 회귀선 그리기
X = np.linspace(0, 1, 100)
Y = (w * X) + b

plt.scatter(DATA.inputs, DATA.outputs, s = 0.3)
plt.plot(X, Y, '-r', linewidth = 1.5)
plt.show()

---

4. Loss Visualization

#Gradient( )에 Loss 추가

def Gradient(x, y, w, b):
    y_hat = Machine(x, w, b)
    
    dw = np.mean((y - y_hat) * (-2 * x))
    db = np.mean((y - y_hat) * (-2))
    Loss = np.mean((y - y_hat)**2)

    return dw, db, Loss

#Learning( )에 Loss 추가

def Learning(x, y, w, b, step):
    dw, db, Loss = Gradient(x, y, w, b)
    
    uw = w - step * dw
    ub = b - step * db
    
    Loss = Loss

    return uw, ub, Loss

w = 2
b = 3
step = 0.001
Error = []

for i in range(0, 1500): #1500번 학습
    uw, ub, Loss = Learning(DATA.inputs, DATA.outputs, w, b, step)

    w = uw
    b = ub
    Error.append(Loss)

Error[0:10] #Loss 감소 확인

plt.plot(Error)
plt.show()

plt.plot(Error[0:50], '.')
plt.show()

plt.plot(Error[1450:1500], '.')
plt.show()