Neural Estimation of Submodular Functions with Applications to Differentiable Subset Selection
Authors: Abir De, Soumen Chakrabarti

Submodular functions and variants, through their ability to characterize diversity and coverage, have emerged as a key tool for data selection and summarization.  Many recent approaches to learn submodular functions suffer from limited expressiveness. In this work, we propose FlexSubNet, a family of flexible neural models for both monotone and non-monotone submodular functions. To fit a latent submodular function from (set, value) observations, our method applies a concave function on modular functions in a recursive manner. We do not draw the concave function from a restricted family, but rather learn from data using a highly expressive neural network that implements a differentiable quadrature procedure. Such an expressive neural model for concave functions may be of independent interest.  Next, we extend this setup to provide a novel characterization of monotone $\alpha$-submodular functions, a recently introduced notion of approximate submodular functions.  We then use this characterization to design a novel neural model for such functions. Finally, we consider learning submodular set functions under distant supervision in the form of  (perimeter, high-value-subset) pairs.  This yields a novel subset selection method based on an order-invariant, yet greedy sampler built around the above neural set functions. Our experiments on synthetic and real data show that FlexSubNet outperforms several baselines.