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Deep Sets
Manzil Zaheer · Satwik Kottur · Siamak Ravanbakhsh · Barnabas Poczos · Ruslan Salakhutdinov · Alexander Smola

Thu Dec 07 11:25 AM -- 11:40 AM (PST) @ Hall C

We study the problem of designing objective models for machine learning tasks defined on finite \emph{sets}. In contrast to the traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets and are invariant to permutations. Such problems are widespread, ranging from the estimation of population statistics, to anomaly detection in piezometer data of embankment dams, to cosmology. Our main theorem characterizes the permutation invariant objective functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

Author Information

Manzil Zaheer (Google)
Satwik Kottur (Carnegie Mellon University)
Siamak Ravanbakhsh (CMU/UBC)
Barnabas Poczos (Carnegie Mellon University)
Ruslan Salakhutdinov (Carnegie Mellon University)
Alexander Smola (Amazon - We are hiring!)

**AWS Machine Learning**

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