Multi-fidelity Stability for Graph Representation Learning

• URL: http://arxiv.org/abs/2111.12865v1
• Date: Thu, 25 Nov 2021 01:33:41 GMT
• Title: Multi-fidelity Stability for Graph Representation Learning
• Authors: Yihan He, Joan Bruna
• Abstract summary: We introduce a weaker uniform generalization termed emphmulti-fidelity stability and give an example. We present lower bounds for the discrepancy between the two types of stability, which justified the multi-fidelity design.
• Score: 38.31487722188051
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the problem of structured prediction with graph representation learning (GRL for short), the hypothesis returned by the algorithm maps the set of features in the \emph{receptive field} of the targeted vertex to its label. To understand the learnability of those algorithms, we introduce a weaker form of uniform stability termed \emph{multi-fidelity stability} and give learning guarantees for weakly dependent graphs. We testify that ~\citet{london2016stability}'s claim on the generalization of a single sample holds for GRL when the receptive field is sparse. In addition, we study the stability induced bound for two popular algorithms: \textbf{(1)} Stochastic gradient descent under convex and non-convex landscape. In this example, we provide non-asymptotic bounds that highly depend on the sparsity of the receptive field constructed by the algorithm. \textbf{(2)} The constrained regression problem on a 1-layer linear equivariant GNN. In this example, we present lower bounds for the discrepancy between the two types of stability, which justified the multi-fidelity design.

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