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we are not suppose to use test set when we r fitting the model to our data. but I noticed in this blog https://blog.keras.io/building-autoencoders-in-keras.html which is very established it uses

  validation_data=(x_test, x_test),

The mnist is split in 3 parts test list(10000 data points) , train list(55000 data point)and validation list(5000 datapoint). in all the tutorial i have seen they use test set when they want to train the model shouldn't they use validation set? I haven't seen ppl use test error in Autoencoders! how can I measure the test error of an autoencoder?

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If you read this thread you will find that:"validation data is not used in the fitting process" and "this data is not passed to the training process so the optimiser doesn't update the parameters with respect to this data".

In autoencoder, this validation_data set is used just for calculating the loss function. So, the test error of an autocencoder is nothing but the output of your selected loss function on this validation set.

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