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Submodular functions and variants, through their ability to characterizediversity and coverage, have emerged as a key tool for data selection andsummarization. Many recent approaches to learn submodular functions suffer fromlimited expressiveness. In this work, we propose FLEXSUBNET, a family offlexible neural models for both monotone and non-monotone submodular functions.To fit a latent submodular function from (set, value) observations, FLEXSUBNETapplies a concave function on modular functions in a recursive manner. We donot draw the concave function from a restricted family, but rather learn fromdata using a highly expressive neural network that implements a differentiablequadrature procedure. Such an expressive neural model for concave functions maybe of independent interest. Next, we extend this setup to provide a novelcharacterization of monotone \alpha-submodular functions, a recently introducednotion of approximate submodular functions. We then use this characterizationto design a novel neural model for such functions. Finally, we considerlearning submodular set functions under distant supervision in the form of(perimeter-set, high-value-subset) pairs. This yields a novel subset selectionmethod based on an order-invariant, yet greedy sampler built around the aboveneural set functions. Our experiments on synthetic and real data show thatFLEXSUBNET outperforms several baselines.

Neural Estimation of Submodular Functions with Applications to Differentiable Subset Selection