Supervised Learning - Linear Regression (multi-variable 2)

Linear Regression (선형회귀) : 데이터들을 가장 잘 표현하는 직선의 방정식을 찾는 것

Data 를 대표하는 hypothesis를 직선의 방정식으로 설정

y1 = W1x1 W2x2 + B1
y2 = W3x1 W4x2 + B2

 

 

 

 

 

Step1) Hypothesis

Hypothesis : Linear Equation(Multi-Variable)

Step2) Cost function 

 

Step3) Training - gradient descent method 

 

 

 

 

Tensorflow

w/ min-max scaling

---

#load module
import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt

 

#input & label (age/BMI and high/low blood pressure)
x_input = tf.constant([[25,22],[25,26],[25,30],[35,22],[35,26],[35,30],[45,22],[45,26],[45,30],
                       [55,22],[55,26],[55,30],[65,22],[65,26],[65,30],[73,22],[73,26],[73,30]], dtype= tf.float32)
labels = tf.constant([[118,72],[125,80],[130,80],[118,76],[126,75],[123,79],[120,80],[124,85],[130,83],
                      [122,78],[125,80],[130,81],[127,75],[130,79],[130,81],[125.5,80],[130,80],[138,82]], dtype= tf.float32)

W = tf.Variable(tf.random.normal((2, 2)), dtype=tf.float32)
B = tf.Variable(tf.random.normal((2,)), dtype=tf.float32)

 

#min-max scaling 
x_input_org = x_input
xmin, xmax = np.min(x_input, axis = 0), np.max(x_input, axis = 0)
x_input = (x_input - xmin)/(xmax-xmin)

 

#Function Generation 

def Hypothesis(x) : 
    return tf.matmul(x,W) + B

def Cost() : 
    return tf.reduce_mean(tf.square(Hypothesis(x_input)-labels))
    
def Predict(x): 
    return Hypothesis((x-xmin)/(xmax-xmin))

 

#Parameter 
epochs = 10000
lr = 0.01
opt = tf.keras.optimizers.SGD(learning_rate=lr)

training_idx = np.arange(0, epochs+1, 1)
cost_graph = np.zeros(epochs+1)


#Training 
for cnt in range(0, epochs+1):
    cost_graph[cnt] = Cost()
    if cnt % (epochs//10) == 0:
        print("[{:>6}] cost={:>6.4}, W = [[{:>7.4} {:>7.4}] [{:>7.4} {:>7.4}]], B = [{:>7.4}{:>7.4}]".
              format(cnt, cost_graph[cnt], W[0,0], W[0,1], W[1,0],W[1,1], B[0],B[1]))
    
    opt.minimize(Cost,[W, B])

#Validation Test
H_x = Hypothesis(x_input)
for x,h,l in zip(x_input_org, H_x, labels):
  print("Age:{}, BMI:{}=>BP:{:>7.4},{:>7.4} [label => {}]".format(x[0],x[1],h[0], h[1],l))

#Prediction 
age = 29.0
BMI = 25.0
test = tf.constant([[age,BMI]], dtype = tf.float32)
print("Age - {}, BMI - {} : {}mmHg".format(age, BMI, Predict(test)))

 

Age - 29.0, BMI - 25.0 : [[121.81335  77.56746]]mmHg

 

#Cost function graph
plt.title("'Cost / Epochs' Graph")
plt.xlabel("Epochs")
plt.ylabel("Cost")
plt.plot(training_idx, cost_graph)
plt.xlim(0, epochs)
plt.grid(True)
plt.semilogy()
plt.show()