You can probably use deep learning even if your data isn't that big

Deep learning models are complex and tricky to train, and I had a hunch that lack of model convergence/difficulties training probably explained the poor performance, not overfitting. We recreated python versions of the Leekasso and MLP used in the original post to the best of our ability, and the code is available here. The MLP used in the original analysis still looks pretty bad for small sample sizes, but our neural nets get essentially perfect accuracy for all sample sizes. A lot of parameters are problem specific (especially the parameters related to SGD) and poor choices will result in misleadingly bad performance.