python - 为什么我在 Ames Housing 数据集上执行的 Tensorflow 线性回归收敛速度非常非常慢？

Question

我正在尝试对 Kaggle 上提供的 Ames Housing 数据集使用线性回归.

我首先删除了许多功能，对数据进行了一些手动清理。然后，我使用以下实现进行训练。

train_size = np.shape(x_train)[0]
valid_size = np.shape(x_valid)[0]
test_size = np.shape(x_test)[0]
num_features = np.shape(x_train)[1]

graph = tf.Graph()
with graph.as_default():

    # Input
    tf_train_dataset = tf.constant(x_train)
    tf_train_labels = tf.constant(y_train)
    tf_valid_dataset = tf.constant(x_valid)
    tf_test_dataset = tf.constant(x_test)

    # Variables
    weights = tf.Variable(tf.truncated_normal([num_features, 1]))
    biases = tf.Variable(tf.zeros([1]))

    # Loss Computation
    train_prediction = tf.matmul(tf_train_dataset, weights) + biases
    loss = tf.losses.mean_squared_error(tf_train_labels, train_prediction)

    # Optimizer
    # Gradient descent optimizer with learning rate = alpha
    alpha = tf.constant(0.000000003, dtype=tf.float64)
    optimizer = tf.train.GradientDescentOptimizer(alpha).minimize(loss)

    # Predictions
    valid_prediction = tf.matmul(tf_valid_dataset, weights) + biases
    test_prediction = tf.matmul(tf_test_dataset, weights) + biases

这就是我的图表的运行方式:

num_steps = 10001

def accuracy(prediction, labels):
    return ((prediction - labels) ** 2).mean(axis=None)

with tf.Session(graph=graph) as session:
    tf.global_variables_initializer().run()
    print('Initialized')
    for step in range(num_steps):
        _, l, predictions = session.run([optimizer, loss, train_prediction])
        if (step % 1000 == 0):
            print('Loss at step %d: %f' % (step, l))
            print('Validation accuracy: %.1f%%' % accuracy(valid_prediction.eval(), y_valid))
     t_pred = test_prediction.eval()
     print('Test accuracy: %.1f%%' % accuracy(t_pred, y_test))

这是我尝试过的:

1. 我尝试过提高学习率。但是，如果我将学习率提高到超出我现在使用的水平，模型将无法收敛，即损失会爆炸到无穷大。

2. 将迭代次数增加到 10,000,000 次。迭代时间越长，损失收敛得越慢(这是可以理解的)。但我距离合理的值(value)还很远。损失通常是一个10位数字

我的图表有问题吗？或者线性回归是一个糟糕的选择，我应该尝试使用另一种算法？非常感谢任何帮助和建议!

Answer 1

工作代码

import csv
import tensorflow as tf
import numpy as np

with open('train.csv', 'rt') as f:
    reader = csv.reader(f)
    your_list = list(reader)

def toFloatNoFail( data ) :
    try :
        return float(data)
    except :
        return 0

data = [ [ toFloatNoFail(x) for x in row ] for row in your_list[1:] ]
data = np.array( data ).astype( float )
x_train = data[:,:-1]
print x_train.shape
y_train = data[:,-1:]
print y_train.shape


num_features = np.shape(x_train)[1]

# Input
tf_train_dataset = tf.constant(x_train, dtype=tf.float32)
tf_train_labels = tf.constant(y_train, dtype=tf.float32)

# Variables
weights = tf.Variable(tf.truncated_normal( [num_features, 1] , dtype=tf.float32))
biases = tf.Variable(tf.constant(0.0, dtype=tf.float32 ))

train_prediction = tf.matmul(tf_train_dataset, weights) + biases

loss = tf.reduce_mean( tf.square( tf.log(tf_train_labels) - tf.log(train_prediction) ))

optimizer = tf.train.GradientDescentOptimizer(1.0).minimize(loss)

num_steps = 10001

def accuracy(prediction, labels):
    return ((prediction - labels) ** 2).mean(axis=None)


with tf.Session() as session:
    tf.global_variables_initializer().run()
    print('Initialized')
    for step in range(num_steps):
        _, l, predictions = session.run([optimizer, loss, train_prediction])
        if (step % 1000 == 0):
            print('Loss at step %d: %f' % (step, l))

重大变更的说明

您的损失函数未针对价格进行缩放。上述损失函数考虑到您实际上只对与原始价格成比例的价格误差感兴趣。因此，对于值(value) 100 万美元的房子来说， Markdown 5,000 美元应该不会像值(value) 5,000 美元的房子 Markdown 5,000 美元那么糟糕。

新的损失函数是:

loss = tf.reduce_mean( tf.square( tf.log(tf_train_labels) - tf.log(train_prediction) ))