[ML] multi-variable linear regression

multi-variable linear regression

x의 값이 여러개이면 위와 같이 여러번 곱해주면 된다. 

하지만 단점이 있다.

값이 100, 1000 ... 너무 많아지면 연산이 매우 복잡해진다.

우리는 이러한 문제를 Matrix를 이용하여 해결할 수 있다.

기본 원리는 아래와 같다. 

Matrix를 사용하면  n개를 편하게 연산할 수 있다.

※ 주의사항

tensorflow 계산할 때는 H(x) = XW로 해주자!

tensorflow 소스

# Lab 4 Multi-variable linear regression
import tensorflow as tf
 
x1_data = [73, 93, 89, 96, 73]
x2_data = [80, 88, 91, 98, 66]
x3_data = [75, 93, 90, 100, 70]
 
y_data = [152, 185, 180, 196, 142]
 
# placeholders for a tensor that will be always fed.
x1 = tf.placeholder(tf.float32)
x2 = tf.placeholder(tf.float32)
x3 = tf.placeholder(tf.float32)
 
Y = tf.placeholder(tf.float32)
 
w1 = tf.Variable(tf.random_normal([1]), name = 'weight1')
w2 = tf.Variable(tf.random_normal([1]), name = 'weight2')
w3 = tf.Variable(tf.random_normal([1]), name = 'weight3')
b = tf.Variable(tf.random_normal([1]), name = 'bias')
 
hypothesis = x1 * w1 + x2 * w2 + x3 * w3 + b
 
# cost/loss function
cost = tf.reduce_mean(tf.square(hypothesis - Y))
 
# MInimize. Need a very small learning rate for this data set
optimizer = tf.train.GradientDescentOptimizer(learning_rate=1e-5)
train = optimizer.minimize(cost)
 
# Launch the grapph in a session.
sess = tf.Session()
# Initializes global variables in the graph.
sess.run(tf.global_variables_initializer())
 
for step in range(2001):
    cost_val, hy_val, _ = sess.run([cost, hypothesis, train],
                                   feed_dict={x1: x1_data, x2: x2_data, x3: x3_data, Y: y_data})
    if step % 10 == 0:
        print(step, "Cost: ", cost_val, "\nPrediction:\n", hy_val)
 

위에 복잡하게 나열한 것을 matrix를 사용하여 간편하게 만듦.

# Lab 4 Multi-variable linear regression
import tensorflow as tf
 
x_data = [[73., 80., 75.],
          [93., 88., 93.],
          [89., 91., 90.],
          [96., 98., 100.],
          [73., 66., 70.]]
y_data = [[152.],
          [185.],
          [180.],
          [196.],
          [142.]]
 
 
# placeholders for a tensor that will be always fed.
X = tf.placeholder(tf.float32, shape=[None, 3])
Y = tf.placeholder(tf.float32, shape=[None, 1])
 
W = tf.Variable(tf.random_normal([3, 1]), name='weight')
b = tf.Variable(tf.random_normal([1]), name='bias')
 
# Hypothesis
hypothesis = tf.matmul(X, W) + b
 
# Simplified cost/loss function
cost = tf.reduce_mean(tf.square(hypothesis - Y))
 
# Minimize
optimizer = tf.train.GradientDescentOptimizer(learning_rate=1e-5)
train = optimizer.minimize(cost)
 
# Launch the graph in a session.
sess = tf.Session()
# Initializes global variables in the graph.
sess.run(tf.global_variables_initializer())
 
for step in range(2001):
    cost_val, hy_val, _ = sess.run(
        [cost, hypothesis, train], feed_dict={X: x_data, Y: y_data})
    if step % 10 == 0:
        print(step, "Cost: ", cost_val, "\nPrediction:\n", hy_val)