Tensorflow多元线性回归不收敛

Question

我正在尝试使用张量流来训练具有正则化的多元线性回归模型.出于某种原因,我无法获得以下代码的训练片段来计算我想用于梯度下降更新的错误.我在设置图表时做错了吗？

def normalize_data(matrix):
    averages = np.average(matrix,0)
    mins = np.min(matrix,0)
    maxes = np.max(matrix,0)
    ranges = maxes - mins
    return ((matrix - averages)/ranges)

def run_regression(X, Y, X_test, Y_test, lambda_value = 0.1, normalize=False, batch_size=10):
    x_train = normalize_data(X) if normalize else X
    y_train = Y
    x_test = X_test
    y_test = Y_test
    session = tf.Session()

    # Calculate number of features for X and Y
    x_features_length = len(X[0])
    y_features_length = len(Y[0])

    # Build Tensorflow graph parts
    x = tf.placeholder('float', [None, x_features_length], name="X")
    y = tf.placeholder('float', [None, y_features_length], name="Y")
    theta = tf.Variable(tf.random_normal([x_features_length, y_features_length], stddev=0.01), name="Theta")
    lambda_val = tf.constant(lambda_value)

    # Trying to implement this way http://openclassroom.stanford.edu/MainFolder/DocumentPage.php?course=MachineLearning&doc=exercises/ex5/ex5.html
    y_predicted = tf.matmul(x, theta, name="y_predicted")
    regularization_cost_part = tf.cast(tf.mul(lambda_val,tf.reduce_sum(tf.pow(theta,2)), name="regularization_param"), 'float')
    polynomial_cost_part = tf.reduce_sum(tf.pow(tf.sub(y_predicted, y), 2), name="polynomial_sum")

    # Set up some summary info to debug
    with tf.name_scope('cost') as scope:
        cost_func = tf.mul(tf.cast(1/(2*batch_size), 'float'), tf.cast(tf.add(polynomial_cost_part, regularization_cost_part), 'float'))
        cost_summary = tf.scalar_summary("cost", cost_func)

    training_func = tf.train.GradientDescentOptimizer(0.03).minimize(cost_func)

    with tf.name_scope("test") as scope:
        correct_prediction = tf.sub(tf.cast(1, 'float'), tf.reduce_mean(tf.sub(y_predicted, y)))
        accuracy = tf.cast(correct_prediction, "float")
        accuracy_summary = tf.scalar_summary("accuracy", accuracy)

    saver = tf.train.Saver()
    merged = tf.merge_all_summaries()
    writer = tf.train.SummaryWriter("/tmp/football_logs", session.graph_def)
    init = tf.initialize_all_variables()

    session.run(init)
    for i in range(0, (len(x_train)/batch_size)):
        session.run(training_func, feed_dict={x: x_train[i*batch_size:i*batch_size+batch_size], y: y_train[i*batch_size:i*batch_size+batch_size]})
        if i % batch_size == 0:
            result = session.run([merged, accuracy], feed_dict={x: x_test, y: y_test})
            writer.add_summary(result[0], i)
            print "step %d, training accuracy %g"%(i, result[1])

    print "test accuracy %g"%session.run(accuracy, feed_dict={x: x_test, y: y_test})

    save_path = saver.save(session, "/tmp/football.ckpt")
    print "Model saved in file: ", save_path
    session.close()

我的输出看起来像这样

step 0, training accuracy 39.1802
step 10, training accuracy 39.1802
step 20, training accuracy 39.1802
...
step 210, training accuracy 39.1802
test accuracy 39.1802
Model saved in file:  /tmp/football.ckpt

Answer 1

这似乎确实是学习率的问题：0.03可能太高，具体取决于您的数据的样子。此外，您可能希望以更明确的方式创建与会话分离的图形，或者如果您的数据集具有中/低维度，甚至可以使用正规方程来达到最佳解决方案而无需迭代。在这里，我发布了一些示例，希望对您有所帮助！此外，TF 教程很好地介绍了它（在该页面中搜索“完整程序”）。

但是关于您的代码，这是一个对我有用的版本：我更改了一些已弃用的函数，并且基本上将学习率设置为低得多的值alpha=1e-8，这（在代码中也生成的合成数据集上）似乎收敛：

test accuracy 2176.11
test accuracy 1898.6
test accuracy 1663.69
test accuracy 1458.53
test accuracy 1287.57
test accuracy 1116.9
test accuracy 969.474
test accuracy 841.028
test accuracy 738.592
test accuracy 649.891
test accuracy 565.188
test accuracy 495.33
test accuracy 438.351
test accuracy 381.161
test accuracy 333.213
test accuracy 289.575
test accuracy 254.394
test accuracy 222.836
test accuracy 197.36
test accuracy 172.788
test accuracy 152.251
test accuracy 132.664
test accuracy 115.982
test accuracy 101.021
final test accuracy 90.2555

代码：

import tensorflow as tf
import numpy as np


# generate some dataset
DIMENSIONS = 5
DS_SIZE = 5000
TRAIN_RATIO = 0.5 # 50% of the dataset isused for training
_train_size = int(DS_SIZE*TRAIN_RATIO)
_test_size = DS_SIZE - _train_size
f = lambda(x): sum(x) # the "true" function: f = 0 + 1*x1 + 1*x2 + 1*x3 ...
noise = lambda: np.random.normal(0,10) # some noise
# training globals
LAMBDA = 1e6 # L2 regularization factor
# generate the dataset, the labels and split into train/test
ds = [[np.random.rand()*1000 for d in range(DIMENSIONS)] for _ in range(DS_SIZE)]
ds = [([1]+x, [f(x)+noise()]) for x in ds] # add x[0]=1 dimension and labels
np.random.shuffle(ds)
train_data, train_labels = zip(*ds[0:_train_size])
test_data, test_labels = zip(*ds[_train_size:])



def normalize_data(matrix):
    averages = np.average(matrix,0)
    mins = np.min(matrix,0)
    maxes = np.max(matrix,0)
    ranges = maxes - mins
    return ((matrix - averages)/ranges)

def run_regression(X, Y, X_test, Y_test, lambda_value = 0.1, normalize=False, batch_size=10, alpha=1e-8):
    x_train = normalize_data(X) if normalize else X
    y_train = Y
    x_test = X_test
    y_test = Y_test
    session = tf.Session()
    # Calculate number of features for X and Y
    x_features_length = len(X[0])
    y_features_length = len(Y[0])
    # Build Tensorflow graph parts
    x = tf.placeholder('float', [None, x_features_length], name="X")
    y = tf.placeholder('float', [None, y_features_length], name="Y")
    theta = tf.Variable(tf.random_normal([x_features_length, y_features_length], stddev=0.01), name="Theta")
    lambda_val = tf.constant(lambda_value)
    # Trying to implement this way http://openclassroom.stanford.edu/MainFolder/DocumentPage.php?course=MachineLearning&doc=exercises/ex5/ex5.html
    y_predicted = tf.matmul(x, theta, name="y_predicted")
    #regularization_cost_part = tf.cast(tf.multiply(lambda_val,tf.reduce_sum(tf.pow(theta,2)), name="regularization_param"), 'float')
    #polynomial_cost_part = tf.reduce_sum(tf.pow(tf.subtract(y_predicted, y), 2), name="polynomial_sum")
    # Set up some summary info to debug
    with tf.name_scope('cost') as scope:
        #cost_func = tf.multiply(tf.cast(1/(2*batch_size), 'float'), tf.cast(tf.add(polynomial_cost_part, regularization_cost_part), 'float'))
        cost_func = (tf.nn.l2_loss(y_predicted - y)+lambda_val*tf.nn.l2_loss(theta))/float(batch_size)
        #DEPRECATED*** cost_summary = tf.scalar_summary("cost", cost_func)
        cost_summary = tf.summary.scalar('cost', cost_func)# Add a scalar summary for the snapshot loss.
    training_func = tf.train.GradientDescentOptimizer(alpha).minimize(cost_func)
    with tf.name_scope("test") as scope:
        correct_prediction = tf.subtract(tf.cast(1, 'float'), tf.reduce_mean(tf.subtract(y_predicted, y)))
        accuracy = tf.cast(correct_prediction, "float")
        #DEPRECATED*** accuracy_summary = tf.scalar_summary("accuracy", accuracy)
        #accuracy_summary = tf.summary.scalar("accuracy", accuracy)
    saver = tf.train.Saver()
    #DEPRECATED*** merged = tf.merge_all_summaries()
    merged = tf.summary.merge_all()
    #DEPRECATED*** writer = tf.train.SummaryWriter("/tmp/football_logs", session.graph_def)
    writer = tf.summary.FileWriter("/tmp/football_logs", session.graph)
    #DEPRECATED*** init = tf.initialize_all_variables()
    init = tf.global_variables_initializer()
    session.run(init)
    for i in range(1, (len(x_train)/batch_size)):
        session.run(training_func, feed_dict={x: x_train[i*batch_size:i*batch_size+batch_size], y: y_train[i*batch_size:i*batch_size+batch_size]})
        if i % batch_size == 0:
            print "test accuracy %g"%session.run(accuracy, feed_dict={x: x_test, y: y_test})
            #result = session.run([merged, accuracy], feed_dict={x: x_test, y: y_test})
            # writer.add_summary(result[0], i)
            # print "step %d, training accuracy %g"%(i, result[1])
            #writer.flush()
    print "final test accuracy %g"%session.run(accuracy, feed_dict={x: x_test, y: y_test})
    # save_path = saver.save(session, "/tmp/football.ckpt")
    # print "Model saved in file: ", save_path
    session.close()

run_regression(train_data, train_labels, test_data, test_labels, normalize=False, alpha=1e-8)

正如我所说，您可能希望更改结构以有利于可读性和可扩展性，但希望这会有所帮助！

干杯，安德烈斯