Tensorflow多元線性回歸不收斂

Question

我正在嘗試使用張量流來訓練具有正則化的多元線性回歸模型。 出於某種原因，我無法獲得以下代碼的訓練片段來計算我想用於梯度下降更新的錯誤。 我在設置圖表時做錯了嗎？

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()

我的輸出看起來像這樣

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

學習率似乎確實存在問題： 0.03可能過高，具體取決於數據的外觀。 此外，如果您的數據集具有中/低維度，您可能希望以更明確的方式創建與會話分離的圖形，或者甚至使用常規方程式來獲得最佳解決方案而無需迭代。 在這里，我發布了一些您可能會發現有用的示例！ 此外， TF教程很好地介紹了它（在該頁面中搜索“完整程序”）。

但是對於你的代碼，這里有一個適合我的版本：我改變了一些不推薦使用的函數，並且基本上將學習速率設置為低得多的值alpha=1e-8 ，其中（在代碼中也生成的合成數據集上）似乎收斂：

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

---

碼：

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)

正如我所說，您可能希望更改結構以支持可讀性和可伸縮性，但希望這會有所幫助！

干杯，安德烈斯