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Stability of Graph Scattering Transforms
Fernando Gama · Alejandro Ribeiro · Joan Bruna

Tue Dec 10 05:30 PM -- 07:30 PM (PST) @ East Exhibition Hall B + C #226

Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to translations, and stable to perturbations that are close to translations. This stability property dons the scattering transform with a robustness to small changes in the metric domain of the data. When considering network data, regular convolutions do not hold since the data domain presents an irregular structure given by the network topology. In this work, we extend scattering transforms to network data by using multi-resolution graph wavelets, whose computation can be obtained by means of graph convolutions. Furthermore, we prove that the resulting graph scattering transforms are stable to metric perturbations of the underlying network. This renders graph scattering transforms robust to changes on the network topology, making it particularly useful for cases of transfer learning, topology estimation or time-varying graphs.

Author Information

Fernando Gama (University of Pennsylvania)

I am a Ph.D. candidate at the Electrical and Systems Engineering department of the University of Pennsylvania. My advisor is Prof. Alejandro Ribeiro. I received an Electronic Engineering degree from the School of Engineering of the University of Buenos Aires, Argentina in 2013, and a M. A. in Statistics from the Wharton School in 2017. I have been a visiting researcher at TU Delft in 2017, and a research intern at Facebook Artificial Intelligence Research in 2018. I was awarded with a Fulbright scholarship for international students for 2014-2016. My research interests currently lie on the field of machine learning for network data. More specifically, I am interested in developing collaborative intelligence. The fundamental objective is for a group of entities (modeled as nodes in a graph; could be team of autonomous agents, sensors in a network, sources in a power grid, vehicles in a transportation network) to learn, from data, how to collaboratively accomplish a certain task. The challenge is that the nodes have access only to partial, local information acquired through exchanges with neighboring nodes, but need to coordinate a global solution for the entire team. To tackle this problem, we have been developing tools within the context of graph neural networks (GNNs). We have been focusing on solutions that can be implemented locally on a given graph, exploiting the fact that nodes have computational capabilities. We have also obtained theoretical results on how the performance of GNNs change when the underlying graph changes. This allows to set limits on transfer learning, and time-varying graphs. Currently, we are researching applications to teams of autonomous agents, power grids and wireless networks.

Alejandro Ribeiro (University of Pennsylvania)
Joan Bruna (NYU)

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