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I am doing some classification work on a set of relatively small dataset, and the model starts to overfit quickly, but there is no way I can get extra data. Can I use a generative adversarial network (GAN) or other generative model to generate data that looks like my dataset but has more diversity or noise, in order to reduce the overfitting of my classifier? Is there any paper on the application of GAN in this subject?

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Sure, it is called Data Augmentation Generating Adversarial Networks. The main idea is to train a GAN on another dataset, in another domain; then use it to conditionally generate examples from the target domain (the one in which is used for classification and is rather small in size of data).

You can similarly train the GAN on your target dataset, but if that is large enough to train a GAN, then you an use it directly for supervised training.

If you have lots of unlabeled data/distribution shift between training and test though, it makes sense to train a GAN on the target dataset as well. The distribution shift solution is explained in the third referenced paper. In other words, if you have generalization problems, it might help.

There are some other papers with similar ideas:

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