TensorFlow 기초 8 - cost와 w(기울기) 구하기(함수 사용 x - 원리 이해)

 

라이브러리에 있는 함수(SGD, RMSprop, Adam)로 자동으로 계산되지만, 원리의 이해를 위해 파이썬으로 작성해 보았다.

# 모델의 정확도가 높을수록 비용함수 값은 낮아진다.
import numpy as na
import math
real = [10, 9, 3, 2, 11] # y 실제값
pred = [11, 5, 2, 4, 3]  # y 예측값(모델에 의해 얻어진 값이라 가정)

cost = 0

for i in range(5):
    cost += math.pow(pred[i] - real[i], 2) # 거듭제곱
    print(cost)

print('cost :', cost / len(pred))

print()
real = [10, 9, 3, 2, 11] # y 실제값
pred = [11, 8, 4, 3, 11] # y 예측값(모델에 의해 얻어진 값이라 가정)

cost = 0

for i in range(5):
    cost += math.pow(pred[i] - real[i], 2) # pow() 함수는 y의 거듭제곱에 대한 x의 값을 계산합니다.
    print(cost)

print('cost :', cost / len(pred))

print('-----------')
# 가중치(W, weight)와 비용함수(cost function, loss, 손실, 비용)의 변화 값을 시각화
import tensorflow as tf
import matplotlib.pyplot as plt

x = [1,2,3,4,5]
y = [1,2,3,4,5]
b = 0

# hypothesis = x * w + b
# cost = tf.reduce_sum(tf.pow(hypothesis - y, 2)) / len(x) # reduce_sum은 합을 구한 뒤 차원을 떨어트린다.
# 비용 함수 = 예측값 - 실제값에 제곱을 하고 그 합에 대한 평균

w_val = []
cost_val = []

for i in range(-30, 50):
    feed_w = i * 0.1 # 0.1은 학습률(기울기)
    # print(feed_w)
    hypothesis = tf.multiply(feed_w, x) + b # 예측값
    cost = tf.reduce_mean(tf.square(hypothesis - y))
    cost_val.append(cost)
    w_val.append(feed_w)
    print(str(i) + ' ' + ', cost :' + str(cost.numpy()) + ', weight :' + str(feed_w))

plt.plot(w_val, cost_val)
plt.xlabel('w')
plt.ylabel('y')
plt.show()



<console>
1.0
17.0
18.0
22.0
86.0
cost : 17.2

1.0
2.0
3.0
4.0
4.0
cost : 0.8
-----------
2022-11-29 16:23:57.775615: I tensorflow/core/platform/cpu_feature_guard.cc:193] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  AVX AVX2
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
-30 , cost :176.0, weight :-3.0
-29 , cost :167.31001, weight :-2.9000000000000004
-28 , cost :158.84, weight :-2.8000000000000003
-27 , cost :150.59, weight :-2.7
-26 , cost :142.55998, weight :-2.6
-25 , cost :134.75, weight :-2.5
-24 , cost :127.16001, weight :-2.4000000000000004
-23 , cost :119.78999, weight :-2.3000000000000003
-22 , cost :112.64, weight :-2.2
-21 , cost :105.71, weight :-2.1
-20 , cost :99.0, weight :-2.0
-19 , cost :92.51, weight :-1.9000000000000001
-18 , cost :86.24, weight :-1.8
-17 , cost :80.19, weight :-1.7000000000000002
-16 , cost :74.36, weight :-1.6
-15 , cost :68.75, weight :-1.5
-14 , cost :63.359997, weight :-1.4000000000000001
-13 , cost :58.190002, weight :-1.3
-12 , cost :53.24, weight :-1.2000000000000002
-11 , cost :48.51, weight :-1.1
-10 , cost :44.0, weight :-1.0
-9 , cost :39.71, weight :-0.9
-8 , cost :35.64, weight :-0.8
-7 , cost :31.789999, weight :-0.7000000000000001
-6 , cost :28.16, weight :-0.6000000000000001
-5 , cost :24.75, weight :-0.5
-4 , cost :21.56, weight :-0.4
-3 , cost :18.59, weight :-0.30000000000000004
-2 , cost :15.839999, weight :-0.2
-1 , cost :13.31, weight :-0.1
0 , cost :11.0, weight :0.0
1 , cost :8.91, weight :0.1
2 , cost :7.04, weight :0.2
3 , cost :5.39, weight :0.30000000000000004
4 , cost :3.9599998, weight :0.4
5 , cost :2.75, weight :0.5
6 , cost :1.7599999, weight :0.6000000000000001
7 , cost :0.99000007, weight :0.7000000000000001
8 , cost :0.43999997, weight :0.8
9 , cost :0.11000004, weight :0.9
10 , cost :0.0, weight :1.0
11 , cost :0.11000004, weight :1.1
12 , cost :0.44000012, weight :1.2000000000000002
13 , cost :0.9899999, weight :1.3
14 , cost :1.7599999, weight :1.4000000000000001
15 , cost :2.75, weight :1.5
16 , cost :3.9600003, weight :1.6
17 , cost :5.3900003, weight :1.7000000000000002
18 , cost :7.0399995, weight :1.8
19 , cost :8.909999, weight :1.9000000000000001
20 , cost :11.0, weight :2.0
21 , cost :13.309999, weight :2.1
22 , cost :15.840001, weight :2.2
23 , cost :18.59, weight :2.3000000000000003
24 , cost :21.560001, weight :2.4000000000000004
25 , cost :24.75, weight :2.5
26 , cost :28.159998, weight :2.6
27 , cost :31.790003, weight :2.7
28 , cost :35.639996, weight :2.8000000000000003
29 , cost :39.710003, weight :2.9000000000000004
30 , cost :44.0, weight :3.0
31 , cost :48.51, weight :3.1
32 , cost :53.24, weight :3.2
33 , cost :58.190002, weight :3.3000000000000003
34 , cost :63.360004, weight :3.4000000000000004
35 , cost :68.75, weight :3.5
36 , cost :74.36, weight :3.6
37 , cost :80.19, weight :3.7
38 , cost :86.24, weight :3.8000000000000003
39 , cost :92.51, weight :3.9000000000000004
40 , cost :99.0, weight :4.0
41 , cost :105.71, weight :4.1000000000000005
42 , cost :112.63999, weight :4.2
43 , cost :119.79, weight :4.3
44 , cost :127.16001, weight :4.4
45 , cost :134.75, weight :4.5
46 , cost :142.55998, weight :4.6000000000000005
47 , cost :150.59, weight :4.7
48 , cost :158.84, weight :4.800000000000001
49 , cost :167.31001, weight :4.9

위와 같은 원리로 cost와 w(기울기)값을 구할 수 있다.

 

 

cost와 w(기울기) 시각화