Supervised Learning - Linear Regression (single-variable)

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

Data 를 대표하는 hypothesis를 직선의 방정식으로 설정

y = Ax + B

 

 

 

 

 

Step1) Hypothesis

 

Step2) Cost function 

 

Step3) Training - gradient descent method 

 

 

 

 

Numpy

w/o min-max scaling

---

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

 

#input & label (age and blood pressure)
x_input = np.array([15,20,25,30,31,35,42,43,45,50,55,56,66,67,68,70,71,73], dtype= np.float32)
labels = np.array([118,125,130,118,126,123,120,124,130,122,125,130,127,130,130,125.5,130,138], dtype= np.float32)

#weight and bias
W = np.random.normal()
B = np.random.normal()

 

#Function Generation 

def Hypothesis(x) : 
    return W*x + B

def Cost() : 
    return np.mean((Hypothesis(x_input)- labels)**2)

def Gradient(x,y): 
    return np.mean(x*(W*x+(B-y))), np.mean((W*x-y+B))
    
def Predict(x): 
    return Hypothesis(x)

 

#Parameter 
epochs = 100000
lr = 0.0005

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//20) == 0: 
        print("[{}] Cost = {}, W = {}, B = {}".format(cnt, Cost(), W,B))
    
    grad_W, grad_B = Gradient(x_input, labels) 
    W -= lr * grad_W
    B -= lr * grad_B

#Prediction 

age = 29.0
print("{} years : {}mmHg".format(age, Predict(age)))

 

29.0 years : 123.037651955064mmHg

 

 

#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()

#labels and prediction graph

plt.title("Labels and Prediction Graph")
plt.xlabel("x input")
plt.ylabel("Labels and Prediction")
plt.scatter(x_input.reshape(-1,), labels.reshape(-1,),color = 'red', label='labels')
plt.plot(x_input.reshape(-1,), Hypothesis(x_input).reshape(-1,), label='predict')
plt.grid(True)
plt.legend(loc='upper left')
plt.show()

 

 

 

 

 

Tensorflow

w/ min-max scaling

---

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

 

#input & label (age and blood pressure)
x_input = tf.constant([15,20,25,30,31,35,42,43,45,50,55,56,66,67,68,70,71,73], dtype= tf.float32)
labels = tf.constant([118,125,130,118,126,123,120,124,130,122,125,130,127,130,130,125.5,130,138], dtype= tf.float32)

#weight and bias
W = tf.Variable(tf.random.normal(()), dtype = tf.float32)
B = tf.Variable(tf.random.normal(()), dtype = tf.float32)

 

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

 

#Function Generation 

def Hypothesis(x) : 
    return tf.add(tf.multiply(x,W),B)

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

 

#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//20) == 0: 
        print("[{}] Cost = {}, W = {}, B = {}".format(cnt, Cost(), W.numpy(), B.numpy()))
        
    
    opt.minimize(Cost, [W,B])

#Prediction 

age = 29.0
print("{} years : {}mmHg".format(age, Predict(age)))

 

29.0 years : 123.12702178955078mmHg

 

#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()

 

 

#labels and prediction graph

plt.title("Labels and Prediction Graph")
plt.xlabel("x input")
plt.ylabel("Labels and Prediction")
plt.scatter(x_input.numpy().reshape(-1,), labels.numpy().reshape(-1,),color = 'red', label='labels')
plt.plot(x_input.numpy().reshape(-1,), Hypothesis(x_input).numpy().reshape(-1,), label='predict')
plt.grid(True)
plt.legend(loc='upper left')
plt.show()

 

 

 

 

 

numpy) 

age : 29

blood pressure : 123.037mmHg

 

tensorflow) 

age : 29

blood pressure : 123.1270mmHg

 

 

	Numpy	Tensorflow
변수	일반 변수 선언	training 할 변수는 tf.variable() 상수는 tf.constant()
구현	np.mean(), *, +	tf.reduce_mean() tf.square()
학습	직접 구현	optimizer, minimize 사용