Supervised Learning - Linear Regression (multi-variable 1)

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

Data 를 대표하는 hypothesis를 직선의 방정식으로 설정

y = W1x1 W2x2 + B

 

 

 

 

 

Step1) Hypothesis

Step2) Cost function 

 

Step3) Training - gradient descent method 

 

 

 

 

Numpy

w/ min-max scaling

---

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

 

#input & label (age/BMI and blood pressure)
x_input = np.array([[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= 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(size=(2, 1))
B = np.random.normal(size=())

 

#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 np.matmul(x,W)+B

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

def Gradient(x,y): 
    global W, B 
    delta = 5e-7
    
    #W gradient
    pres_W = W.copy()
    grad_W = np.zeros_like(W)
    
    for i in range(W.size):
        W[i,0] = pres_W[i,0] + delta
        cost_p = Cost()
        W[i,0] = pres_W[i,0] - delta
        cost_m = Cost() 
        
        grad_W[i,0] = (cost_p - cost_m)/(2*delta)
        W[i,0] = pres_W[i,0]
    
    #B gradient
    pres_b = B
    B = pres_b + delta
    cost_p = Cost()
    B = pres_b - delta
    cost_m = Cost()
    grad_B = (cost_p-cost_m)/(2*delta)
    B = pres_b
    
    return grad_W, grad_B

    
def Predict(x): 
    return Hypothesis((x-xmin)/(xmax-xmin))

 

#Parameter 
epochs = 1000
lr = 0.05

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("[{:>7}] Cost = {:>10.4}, W = [[{:>7.4}] [{:>7.4}]], B = {:>7.4}".format(cnt, Cost(),  W[0,0], W[1,0],B))
    
    grad_W, grad_B = Gradient(x_input, labels) 
    W -= lr * grad_W
    B -= lr * grad_B

#Prediction 
age = 29.0
BMI = 25.0

print("Age - {}, BMI - {} : {}mmHg".format(age, BMI, Predict([age, BMI])))

 

Age - 29.0, BMI - 25.0 : [121.81400206]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()

#for surface
x_range = np.arange(0,1,0.01)
y_range = np.arange(0,1,0.01)

X, Y = np.meshgrid(x_range, y_range)
Z = X*W[0,0] + Y*W[1,0] + B


#plotting
fig = plt.figure()
ax = fig.add_subplot(111,projection = '3d')
ax.scatter(x_input[:,0], x_input[:,1], labels, c = 'red', marker = 'o', alpha = 0.5)
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, alpha = 0.5)
ax.set_xlabel('scaled Age')
ax.set_ylabel('scaled BMI')
ax.set_zlabel('Blood Pressure')
plt.title('Data and Regression surface')
plt.show()

 

Tensorflow

w/ min-max scaling

---

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

 

#input & label (age/BMI and 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],[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((2, 1)), dtype=tf.float32)
B = tf.Variable(tf.random.normal(()), 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 = 5000
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("[{:>6}] cost = {:>10.4}, W = [ {:>7.4} {:>7.4} ], B = {:>7.4}".format(cnt, cost_graph[cnt], W[0,0], W[1,0], B.numpy()))
    
    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 : {:>7.4} => BP : {:>7.4} [label => {}]".format(x[0],x[1],h[0],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 : [[121.81373]]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()

#for surface
x_range = np.arange(0,1,0.01)
y_range = np.arange(0,1,0.01)

X, Y = np.meshgrid(x_range, y_range)
Z = X*W[0,0] + Y*W[1,0] + B


#plotting
fig = plt.figure()
ax = fig.add_subplot(111,projection = '3d')
ax.scatter(x_input[:,0], x_input[:,1], labels, c = 'red', marker = 'o', alpha = 0.5)
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, alpha = 0.5)
ax.set_xlabel('scaled Age')
ax.set_ylabel('scaled BMI')
ax.set_zlabel('Blood Pressure')
plt.title('Data and Regression surface')
plt.show()

 

 

numpy) 

age : 29

BMI : 25

blood pressure : 121.814mmHg

 

tensorflow) 

age : 29

BMI : 25

blood pressure : 123.814mmHg

 

 

	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