tensorflow deep neural network for regression always predict same results in one batch

Question

I use a tensorflow to implement a simple multi-layer perceptron for regression. The code is modified from standard mnist classifier, that I only changed the output cost to MSE (use tf.reduce_mean(tf.square(pred-y))), and some input, output size settings. However, if I train the network using regression, after several epochs, the output batch are totally the same. for example:

target: 48.129, estimated: 42.634
target: 46.590, estimated: 42.634
target: 34.209, estimated: 42.634
target: 69.677, estimated: 42.634
......

I have tried different batch size, different initialization, input normalization using sklearn.preprocessing.scale (my inputs range are quite different). However, none of them worked. I have also tried one of sklearn example from Tensorflow (Deep Neural Network Regression with Boston Data). But I got another error in line 40:

'module' object has no attribute 'infer_real_valued_columns_from_input'

Anyone has clues on where the problem is? Thank you

My code is listed below, may be a little bit long, but very straghtforward:

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import tensorflow as tf
from tensorflow.contrib import learn
import matplotlib.pyplot as plt

from sklearn.pipeline import Pipeline
from sklearn import datasets, linear_model
from sklearn import cross_validation
import numpy as np

boston = learn.datasets.load_dataset('boston')
x, y = boston.data, boston.target
X_train, X_test, Y_train, Y_test = cross_validation.train_test_split(
x, y, test_size=0.2, random_state=42)

total_len = X_train.shape[0]

# Parameters
learning_rate = 0.001
training_epochs = 500
batch_size = 10
display_step = 1
dropout_rate = 0.9
# Network Parameters
n_hidden_1 = 32 # 1st layer number of features
n_hidden_2 = 200 # 2nd layer number of features
n_hidden_3 = 200
n_hidden_4 = 256
n_input = X_train.shape[1]
n_classes = 1

# tf Graph input
x = tf.placeholder("float", [None, 13])
y = tf.placeholder("float", [None])

# Create model
def multilayer_perceptron(x, weights, biases):
    # Hidden layer with RELU activation
    layer_1 = tf.add(tf.matmul(x, weights['h1']), biases['b1'])
    layer_1 = tf.nn.relu(layer_1)

    # Hidden layer with RELU activation
    layer_2 = tf.add(tf.matmul(layer_1, weights['h2']), biases['b2'])
    layer_2 = tf.nn.relu(layer_2)

    # Hidden layer with RELU activation
    layer_3 = tf.add(tf.matmul(layer_2, weights['h3']), biases['b3'])
    layer_3 = tf.nn.relu(layer_3)

    # Hidden layer with RELU activation
    layer_4 = tf.add(tf.matmul(layer_3, weights['h4']), biases['b4'])
    layer_4 = tf.nn.relu(layer_4)

    # Output layer with linear activation
    out_layer = tf.matmul(layer_4, weights['out']) + biases['out']
    return out_layer

# Store layers weight & bias
weights = {
    'h1': tf.Variable(tf.random_normal([n_input, n_hidden_1], 0, 0.1)),
    'h2': tf.Variable(tf.random_normal([n_hidden_1, n_hidden_2], 0, 0.1)),
    'h3': tf.Variable(tf.random_normal([n_hidden_2, n_hidden_3], 0, 0.1)),
    'h4': tf.Variable(tf.random_normal([n_hidden_3, n_hidden_4], 0, 0.1)),
    'out': tf.Variable(tf.random_normal([n_hidden_4, n_classes], 0, 0.1))
}
biases = {
    'b1': tf.Variable(tf.random_normal([n_hidden_1], 0, 0.1)),
    'b2': tf.Variable(tf.random_normal([n_hidden_2], 0, 0.1)),
    'b3': tf.Variable(tf.random_normal([n_hidden_3], 0, 0.1)),
    'b4': tf.Variable(tf.random_normal([n_hidden_4], 0, 0.1)),
    'out': tf.Variable(tf.random_normal([n_classes], 0, 0.1))
}

# Construct model
pred = multilayer_perceptron(x, weights, biases)

# Define loss and optimizer
cost = tf.reduce_mean(tf.square(pred-y))
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate).minimize(cost)

# Launch the graph
with tf.Session() as sess:
    sess.run(tf.initialize_all_variables())

    # Training cycle
    for epoch in range(training_epochs):
        avg_cost = 0.
        total_batch = int(total_len/batch_size)
        # Loop over all batches
        for i in range(total_batch-1):
            batch_x = X_train[i*batch_size:(i+1)*batch_size]
            batch_y = Y_train[i*batch_size:(i+1)*batch_size]
            # Run optimization op (backprop) and cost op (to get loss value)
            _, c, p = sess.run([optimizer, cost, pred], feed_dict={x: batch_x,
                                                          y: batch_y})
            # Compute average loss
            avg_cost += c / total_batch

        # sample prediction
        label_value = batch_y
        estimate = p
        err = label_value-estimate
        print ("num batch:", total_batch)

        # Display logs per epoch step
        if epoch % display_step == 0:
            print ("Epoch:", '%04d' % (epoch+1), "cost=", \
                "{:.9f}".format(avg_cost))
            print ("[*]----------------------------")
            for i in xrange(3):
                print ("label value:", label_value[i], \
                    "estimated value:", estimate[i])
            print ("[*]============================")

    print ("Optimization Finished!")

    # Test model
    correct_prediction = tf.equal(tf.argmax(pred, 1), tf.argmax(y, 1))
    # Calculate accuracy
    accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))
    print ("Accuracy:", accuracy.eval({x: X_test, y: Y_test}))

Answer 1

Short answer:

Transpose your pred vector using tf.transpose(pred).

Longer answer:

The problem is that pred (the predictions) and y (the labels) are not of the same shape: one is a row vector and the other a column vector. Apparently when you apply an element-wise operation on them, you'll get a matrix, which is not what you want.

The solution is to transpose the prediction vector using tf.transpose() to get a proper vector and thus a proper loss function. Actually, if you set the batch size to 1 in your example you'll see that it works even without the fix, because transposing a 1x1 vector is a no-op.

I applied this fix to your example code and observed the following behaviour. Before the fix:

Epoch: 0245 cost= 84.743440580
[*]----------------------------
label value: 23 estimated value: [ 27.47437096]
label value: 50 estimated value: [ 24.71126747]
label value: 22 estimated value: [ 23.87785912]

And after the fix at the same point in time:

Epoch: 0245 cost= 4.181439120
[*]----------------------------
label value: 23 estimated value: [ 21.64333534]
label value: 50 estimated value: [ 48.76105118]
label value: 22 estimated value: [ 24.27996063]

You'll see that the cost is much lower and that it actually learned the value 50 properly. You'll have to do some fine-tuning on the learning rate and such to improve your results of course.