Questions

[jingw222]

I've been following along your wonderful book for quite a while, and it's a great treasure for the whole community. But there're a couple of questions I've run into recently:

1. In Execution Phase of Char 10, it says 'Next, at the end of each epoch, the code evaluates the model on the last mini-batch and on the full training set, and it prints out the result. Finally, the model parameters are saved to disk.' However, the code evaluating the training set is only feeded with the last batch_size training data, which confuses me a lot. Why do you evaluate only the last batch training set instead of the whole training set (X_train, y_train)?

2. It always baffles me that how do make sure all the batches in one epoch make up the whole training set? I don't know how mnist.train.next_batch() inside, but could you explain a little bit about the fetch_batch():

def fetch_batch(epoch, batch_index, batch_size):

    rnd.seed(epoch * n_batches + batch_index)

    indices = rnd.randint(m, size=batch_size)

    X_batch = scaled_housing_data_plus_bias[indices]

    y_batch = housing.target.reshape(-1, 1)[indices]

    return X_batch, y_batch

What are the batches you sample with the seeds like? To be more specific, do the batches have overlapping instances? And is it correct to assume that all the batches in one epoch consist of all the samples?

[ageron]

Hi @jingw222,

Thanks a lot, I'm really glad you find my book useful. :)

Regarding your first question, there's an error in the text, sorry about that, it should read "on the last mini-batch and on the full test set" (it's listed in the errata page). You could evaluate the training error on the full training set rather than just on the last mini-batch, the only reason I did not do that is because it was very slow, but it would of course be more accurate.

Regarding your second question, you have two options when implementing fetch_batch():

• option 1: you shuffle the training set at the beginning of each epoch, you chop it into disjoint mini-batches of batch_size instances each, and then you return these mini-batches one by one for each training iteration of this epoch. With this option, mini-batches do not overlap during the epoch, and all training instances are fed to the training algorithm at each epoch.
• option 2: you simply pick batch_size instances randomly from the training set, at each training iteration, meaning you don't really care about the epoch number, it's just a rough measure of how many times the model was fed the training set. This solution implies that mini-batches may have overlapping instances, and some instances will almost certainly be left out during a particular epoch (in fact, it's possible to estimate that roughly 36% of the instances will be left out at each epoch).

Option 1 seems better, but in practice option 2 is actually just as good and simpler to implement.

Hope this helps!

[jingw222]

Thanks a lot for your detailed explanation. I cannot be more grateful for that. Here's my dummy example:

Let's just assume we have a training set with index range(0, 10) (so m=10 in this case), epoch=0, n_batches=2and therefore batch_size=5.

So, then rnd.seed(0*2+0); rnd.randint(10, size=5) gives me array([5, 0, 3, 3, 7]), and rnd.seed(0*2+1); rnd.randint(10, size=5) outputs array([5, 8, 9, 5, 0]). Basically, not only does these two batches not contain the whole range, but they can have replacements themselves. Am I doing it wrong?

[ageron]

You're welcome. You're doing it right, this is just one possible technique (option 2), which indeed means that a particular batch may have the same instance multiple times (but it will be very rare for large datasets and small batches). If you want to implement option 1 instead, here's one approach:

import numpy as np

# Create dummy training set
m = 50
n = 2
X_train = np.arange(m * n).reshape(m, n)
y_train = np.arange(m)

# Start training
n_epochs = 3
n_batches = 10
for epoch in range(n_epochs):
    indices = np.random.permutation(50)
    for batch_indices in np.array_split(indices, n_batches):
        X_batch = X_train[batch_indices]
        y_batch = y_train[batch_indices]
        print(X_batch, y_batch) # train on batch

[jingw222]

Great help! I really learned a lot. Thank you very much indeed. And I'm going to continue to dive into the book. :D

[ageron]

You're welcome! Closing this issue.
Cheers, Aurélien