Enhancing selectivity using Wasserstein distance based reweighing

Given two labeled data-sets $\mathcal{S}$ and $\mathcal{T}$, we design a simple and efficient greedy algorithm to reweigh the loss function such that the limiting distribution of the neural network weights that result from training on $\mathcal{S}$ approaches the limiting distribution that would have resulted by training on $\mathcal{T}$. On the theoretical side, we prove that when the metric entropy of the input data-sets is bounded, our greedy algorithm outputs a close to optimal reweighing, i.e., the two invariant distributions of network weights will be provably close in total variation distance. Moreover, the algorithm is simple and scalable, and we prove bounds on the efficiency of the algorithm as well. Our algorithm can deliberately introduce distribution shift to perform (soft) multi-criteria optimization. As a motivating application, we train a neural net to recognize small molecule binders to MNK2 (a MAP Kinase, responsible for cell signaling) which are non-binders to MNK1 (a highly similar protein). We tune the algorithm's parameter so that overall change in holdout loss is negligible, but the selectivity, i.e., the fraction of top 100 MNK2 binders that are MNK1 non-binders, increases from 54\% to 95\%, as a result of our reweighing. Of the 43 distinct small molecules predicted to be most selective from the enamine catalog, 2 small molecules were experimentally verified to be selective, i.e., they reduced the enzyme activity of MNK2 below 50\% but not MNK1, at 10$\mu$M -- a 5\% success rate.