[英]Tensorflow Linear Regression not converging to correct cost
我正在嘗試在張量流中實現多元線性回歸(使用Boston Housing Dataset),但似乎我的成本函數正在收斂並且值不正確(在我的情況下為24000)。 我嘗試擴展功能,但仍然無法正常工作。 關於我在做什么錯的任何想法嗎? 這是代碼:
from sklearn.datasets import load_boston
import numpy as np
import pandas as pd
import tensorflow as tf
from sklearn.cross_validation import train_test_split
import matplotlib.pyplot as plt
from sklearn.metrics import r2_score
from sklearn.preprocessing import MinMaxScaler
rate = 0.000000011
epochs = 100
errors = []
def load_data():
boston = load_boston()
bos = pd.DataFrame(boston.data)
output = pd.DataFrame(boston.target)
return [bos, output]
xS, yS = load_data()
m = len(yS)
x_train, x_test, y_train, y_test = train_test_split(xS, yS, test_size=0.2)
scaler = MinMaxScaler()
scaler.fit(x_train)
x_train = scaler.transform(x_train)
x_test = scaler.transform(x_test)
theta = tf.Variable(tf.zeros([len(xS.columns), 1]))
X = tf.placeholder(tf.float32, shape=[m, len(xS.columns)])
y = tf.placeholder(tf.float32, shape=[m, 1])
b = tf.Variable(tf.zeros([m, 1]))
model = tf.matmul(tf.transpose(theta), tf.transpose(X)) + b
cost = tf.reduce_sum(tf.square(y-model))/(2*m)
optimizer = tf.train.GradientDescentOptimizer(rate).minimize(cost)
init = [tf.global_variables_initializer(), tf.local_variables_initializer()]
with tf.Session() as sess:
sess.run(init)
for e in range(epochs):
sess.run(optimizer, feed_dict={X:xS, y:yS})
loss = sess.run(cost, feed_dict={X:xS, y:yS})
print("cost at step", e, loss)
errors.append(loss)
if errors[len(errors)-1] > errors[len(errors)-2]:
break
theta_temp = np.array(sess.run(theta))
b_temp = np.array(sess.run(b))
plt.plot(list(range(len(errors))), errors)
plt.show()
h = np.transpose(np.add(np.matmul(np.transpose(theta_temp), np.transpose(xS)), np.transpose(b_temp)))
print(r2_score(h, yS))
您正在正確地執行大多數操作。 我將建議您對代碼進行以下更改。
model = tf.matmul(X, theta) + b
以0.001和epoch 1000的學習率進行嘗試,請報告結果。
在你做的情況下
model = tf.matmul(tf.transpose(theta), tf.transpose(X)) + b
你在弄錯。 右側的第一部分的大小為(1,m),第二部分的大小為(m,1)。 然后,由於不期望的廣播,您將獲得一些結果。 這就是為什么您看到學習率僅為0.01或0.1的非常差的結果的原因。
我的第二個建議是刪除中斷標准。
if errors[len(errors)-1] > errors[len(errors)-2]: break
隨機梯度很嘈雜。 沒有證據表明,如果您沿較小的梯度方向前進,那么總會降低成本(也許對這個凸問題確實如此,但我必須思考)。
from sklearn.datasets import load_boston
import numpy as np
import pandas as pd
import tensorflow as tf
from sklearn.cross_validation import train_test_split
import matplotlib.pyplot as plt
from sklearn.metrics import r2_score
from sklearn.preprocessing import MinMaxScaler
rate = 0.1
epochs = 100
errors = []
def load_data():
boston = load_boston()
bos = pd.DataFrame(boston.data)
output = pd.DataFrame(boston.target)
return [bos, output]
xS, yS = load_data()
x_train, x_test, y_train, y_test = train_test_split(xS, yS, test_size=0.2)
m = len(y_train)
scaler = MinMaxScaler()
scaler.fit(x_train)
x_train = scaler.transform(x_train)
x_test = scaler.transform(x_test)
theta = tf.Variable(tf.zeros([len(xS.columns), 1]))
X = tf.placeholder(tf.float32, shape=[m, len(xS.columns)])
y = tf.placeholder(tf.float32, shape=[m, 1])
b = tf.Variable(tf.zeros([1]))
model = tf.matmul(X, theta) + b
cost = tf.reduce_sum(tf.square(y-model))/(2*m)
optimizer = tf.train.GradientDescentOptimizer(rate).minimize(cost)
init = [tf.global_variables_initializer(), tf.local_variables_initializer()]
with tf.Session() as sess:
sess.run(init)
for e in range(epochs):
sess.run(optimizer, feed_dict={X:x_train, y:y_train})
loss = sess.run(cost, feed_dict={X:x_train, y:y_train})
print("cost at step", e, loss)
errors.append(loss)
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