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Suppose that we have a network which performs poorly on the training set, something like ~40% accuracy.

Does it make any sense at all to add a regularisation term in such case? Isn't it only needed when overfitting occurs?

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  • $\begingroup$ I think you need to describe the problem in more detail. $\endgroup$ – Michael R. Chernick Apr 8 '17 at 18:47
  • $\begingroup$ If you can only reach 40% accuracy on your training set, it seems like something is wrong with either your model or the optimization procedure, hence overfitting won't be the first of your concerns. $\endgroup$ – galoosh33 Apr 8 '17 at 19:00
  • $\begingroup$ @galoosh33 it's not a problem actually, the model is pretty simple for this problem that's why the low accuracy. The question is more theoretical. $\endgroup$ – Tnp Moe Apr 8 '17 at 20:28
  • $\begingroup$ @MichaelChernick The question is more theoretical, that is, I have a simple model that performs ~40% on training set. The thing is that by adding more and more regularisation there is actually no gains on the test set. The accuracy is always less on all sets (train/val/test). $\endgroup$ – Tnp Moe Apr 8 '17 at 20:30
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You can't tell from your model's performance on the training data whether you have overfit. Even your "poor" accuracy of 40% may be due to overfitting and may not generalize. You can't tell a priori what is poor and what isn't. So you might indeed be able to improve your out-of-sample accuracy through regularization.

I'd suggest you partition your data. Fit your model on 75%. Record your in-sample accuracy on these 75%, as well as the out-of-sample accuracy on the remaining 25%. Do this multiple times with different randomly sampled 75%. Your out-of-sample accuracy will usually be lower than in-sample, but if it is often "much" lower, that might be an indicator of overfitting. ("much" is not easily quantified.) In such a case, regularization might be helpful.

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  • $\begingroup$ I don't see how overfitting on training set will reduce training set accuracy. $\endgroup$ – Tnp Moe Apr 8 '17 at 18:58
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    $\begingroup$ I didn't claim that. Overfitting might reduce out-of-sample accuracy. $\endgroup$ – Stephan Kolassa Apr 8 '17 at 19:02

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