LinearRegression_Example

4개의 입력데이터 연산 (A1-A2+A3-A4) 예측하는 Linear Regression Batch 예제

data definition

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import numpy as np
from datetime import datetime

loaded_data = np.loadtxt('./sps.csv', delimiter=',', dtype=np.float32)

x_data = loaded_data[ :, 1:]
t_data = loaded_data[ :, [0]]

# 데이터 차원 및 shape 확인
print("loaded_data.ndim = ", loaded_data.ndim, ", loaded_data.shape = ", loaded_data.shape)
print("x_data.ndim = ", x_data.ndim, ", x_data.shape = ", x_data.shape)
print("t_data.ndim = ", t_data.ndim, ", t_data.shape = ", t_data.shape) 

loaded_data.ndim =  2 , loaded_data.shape =  (50, 5)
x_data.ndim =  2 , x_data.shape =  (50, 4)
t_data.ndim =  2 , t_data.shape =  (50, 1)

initialize weights and bias

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np.random.seed(0)

W = np.random.rand(4,1)  # 4X1 행렬
b = np.random.rand(1)  
print("W = ", W, ", W.shape = ", W.shape, ", b = ", b, ", b.shape = ", b.shape)

W =  [[0.5488135 ]
 [0.71518937]
 [0.60276338]
 [0.54488318]] , W.shape =  (4, 1) , b =  [0.4236548] , b.shape =  (1,)

define loss function and output, y

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def loss_func(x, t):
    
    y = np.dot(x,W) + b
    
    return ( np.sum( (t - y)**2 ) ) / ( len(x) )

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def numerical_derivative(f, x):
    delta_x = 1e-4 # 0.0001
    grad = np.zeros_like(x)
    
    it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
    
    while not it.finished:
        idx = it.multi_index        
        tmp_val = x[idx]
        x[idx] = float(tmp_val) + delta_x
        fx1 = f(x) # f(x+delta_x)
        
        x[idx] = float(tmp_val) - delta_x 
        fx2 = f(x) # f(x-delta_x)
        grad[idx] = (fx1 - fx2) / (2*delta_x)
        
        x[idx] = tmp_val 
        it.iternext()   
        
    return grad

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# 손실함수 값 계산 함수
# 입력변수 x, t : numpy type
def error_val(x, t):
    y = np.dot(x,W) + b
    
    return ( np.sum( (t - y)**2 ) ) / ( len(x) )

learning

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learning_rate = 1e-3  # 

f = lambda x : loss_func(x_data,t_data)

print("Initial error value = ", error_val(x_data, t_data), "Initial W = ", W, "\n", ", b = ", b )

start_time = datetime.now()

for step in  range(30001):    # 3만번 반복수행
    
    W -= learning_rate * numerical_derivative(f, W)
    
    b -= learning_rate * numerical_derivative(f, b)
   
    if (step % 500 == 0):
        print("step = ", step, "error value = ", error_val(x_data, t_data) )
        
end_time = datetime.now()
        
print("")
print("Elapsed Time => ", end_time - start_time)

Initial error value =  64.38302549674624 Initial W =  [[0.5488135 ]
 [0.71518937]
 [0.60276338]
 [0.54488318]] 
 , b =  [0.4236548]
step =  0 error value =  60.604776072341444
step =  500 error value =  0.01167190429026227
step =  1000 error value =  0.004047845907167936
step =  1500 error value =  0.0014043526649038332
step =  2000 error value =  0.00048722369128301977
step =  2500 error value =  0.00016903654707396402
step =  3000 error value =  5.864524808192556e-05
step =  3500 error value =  2.0346281216250795e-05
step =  4000 error value =  7.0589037112171215e-06
step =  4500 error value =  2.4490038781355694e-06
step =  5000 error value =  8.496531813563435e-07
step =  5500 error value =  2.9477720922949027e-07
step =  6000 error value =  1.0226949652836696e-07
step =  6500 error value =  3.5481202727676135e-08
step =  7000 error value =  1.230978727513882e-08
step =  7500 error value =  4.2707363649495105e-09
step =  8000 error value =  1.4816819081469759e-09
step =  8500 error value =  5.14052165565946e-10
step =  9000 error value =  1.7834437166114527e-10
step =  9500 error value =  6.187448869478846e-11
step =  10000 error value =  2.1466628382414438e-11
step =  10500 error value =  7.447595024911832e-12
step =  11000 error value =  2.583855772566766e-12
step =  11500 error value =  8.964384646654429e-13
step =  12000 error value =  3.1100881478795545e-13
step =  12500 error value =  1.0790086188891214e-13
step =  13000 error value =  3.7434938904037783e-14
step =  13500 error value =  1.2987613159065e-14
step =  14000 error value =  4.5059000875171345e-15
step =  14500 error value =  1.5632692166840009e-15
step =  15000 error value =  5.423579204531311e-16
step =  15500 error value =  1.8816472159910655e-16
step =  16000 error value =  6.528154409141282e-17
step =  16500 error value =  2.2648666703984575e-17
step =  17000 error value =  7.857690960008845e-18
step =  17500 error value =  2.726133322193127e-18
step =  18000 error value =  9.458002967175832e-19
step =  18500 error value =  3.2813425922981097e-19
step =  19000 error value =  1.1384228300504383e-19
step =  19500 error value =  3.9496353646178484e-20
step =  20000 error value =  1.370281435831186e-20
step =  20500 error value =  4.754125218582716e-21
step =  21000 error value =  1.6494531600977032e-21
step =  21500 error value =  5.723172523227641e-22
step =  22000 error value =  1.9859337893496504e-22
step =  22500 error value =  6.893889116469676e-23
step =  23000 error value =  2.3940569803507154e-23
step =  23500 error value =  8.318580669294951e-24
step =  24000 error value =  2.8926538754400545e-24
step =  24500 error value =  1.007017095562386e-24
step =  25000 error value =  3.5189776953551637e-25
step =  25500 error value =  1.2368469252287204e-25
step =  26000 error value =  4.4692299850792143e-26
step =  26500 error value =  1.692665607750921e-26
step =  27000 error value =  6.981567293526183e-27
step =  27500 error value =  3.257963561703718e-27
step =  28000 error value =  1.7847429561181468e-27
step =  28500 error value =  1.1894827601256653e-27
step =  29000 error value =  9.176150809230155e-28
step =  29500 error value =  7.812023703927484e-28
step =  30000 error value =  7.296706880293302e-28

Elapsed Time =>  0:00:06.304803

In [ ]:

print(W)
print(b)

[[ 1.]
 [-1.]
 [ 1.]
 [-1.]]
[2.38435128e-14]

evaluate and predict

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# 학습을 마친 후, 임의의 데이터에 대해 미래 값 예측 함수
# 입력변수 x : numpy type

def predict(x):
    y = np.dot(x,W) + b
    
    return y

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ex_data_01 = np.array([4, 4, 4, 4])    #  4 - 4 + 4 - 4 = 0

print("predicted value = ", predict(ex_data_01) ) 

predicted value =  [-3.21117277e-14]

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ex_data_02 = np.array([-3, 0, 9, -1])    #  -3 -0 +9 -(-1) = 7

print("predicted value = ", predict(ex_data_02) ) 

predicted value =  [7.]

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ex_data_03 = np.array([-7, -9, -2, 8])   # -7 -(-9) + (-2) -8 = -8

print("predicted value = ", predict(ex_data_03) ) 

predicted value =  [-8.]

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ex_data_04 = np.array([1, -2, 3, -2])   # 1 -(-2) + 3 -(-2) = 8

print("predicted value = ", predict(ex_data_04) ) 

predicted value =  [8.]

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ex_data_05 = np.array([19, -12, 0, -76])   # 19 -(-12) + 0 -(-76) = 107

print("predicted value = ", predict(ex_data_05) ) 

predicted value =  [107.]

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ex_data_06 = np.array([2001, -1, 109, 31])   # 2001 -(-1) + 109 -(31) = 2080

print("predicted value = ", predict(ex_data_06) ) 

predicted value =  [2080.]

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ex_data_07 = np.array([99999, -8911, 10009, 1231331])   # 99999 -(-8911) + 10009 -(1231331) = -1112412

print("predicted value = ", predict(ex_data_07) ) 

predicted value =  [-1112412.00000001]

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