We devise methods for learning functions indexed by non-Euclidean domains such as directed graphs, powersets of finite sets, lattices and partially ordered sets. Furthermore, we port deep learning architectures to these index domains. In order to do so, we draw inspiration from our new signal processing frameworks (e.g., for set functions or for lattice data). Our new signal processing frameworks provide the mathematical tools to incorporate the structure of non-Euclidean index domains into machine learning methods. For example, the Fourier basis associated with a non-Euclidean domain naturally defines a feature space embedding suitable for learning linear models, and the associated generalized convolution can be used port convolutional neural networks to the non-Euclidean domain.

References

  1. Vedran Mihal, Bastian Seifert, Markus Püschel
    Porting Signal Processing from Undirected to Directed Graphs: Case Study Signal Denoising with Unrolling Networks
    submitted for publication

  2. Chris Wendler, Andisheh Amrollahi, Bastian Seifert, Andreas Krause, Markus Püschel
    Learning Set Functions that are Sparse in Non-Orthogonal Fourier Bases
    to appear in Proc. AAAI Conference on Artificial Intelligence, 2021

  3. Jakob Weissteiner, Chris Wendler, Sven Seuken, Ben Lubin, Markus Püschel
    Fourier Analysis-based Iterative Combinatorial Auctions
    submitted for publication

  4. Chris Wendler, Dan Alistarh and Markus Püschel
    Powerset Convolutional Neural Networks
    Proc. Neural Information Processing Systems (NeurIPS), 2019