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Shape Constraints for Set Functions
Andrew Cotter · Maya Gupta · Heinrich Jiang · Erez Louidor · James Muller · Taman Narayan · Serena Wang · Tao Zhu

Tue Jun 11 12:05 PM -- 12:10 PM (PDT) @ Seaside Ballroom

Set functions predict a label from a permutation-invariant variable-size collection of feature vectors. We propose making set functions more understandable and regularized by capturing domain knowledge through shape constraints. We show how prior work in monotonic constraints can be adapted to set functions. Then we propose two new shape constraints designed to generalize the conditioning role of weights in a weighted mean. We show how one can train standard functions and set functions that satisfy these shape constraints with a deep lattice network. We propose a nonlinear estimation strategy we call the semantic feature engine that uses set functions with the proposed shape constraints to estimate labels for compound sparse categorical features. Experiments on real-world data show the achieved accuracy is similar to deep sets or deep neural networks, but provides guarantees of the model behavior and is thus easier to explain and debug.

Author Information

Andrew Cotter (Google AI)
Maya Gupta (Google)
Heinrich Jiang (Google Research)
Erez Louidor (Google, Inc.)
James Muller (Google)
Taman Narayan (Google)
Serena Wang (Google)
Tao Zhu (Google)

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