Graph Convolution for Semi-Supervised Classification: Improved Linear Separability and Out-of-Distribution Generalization

• URL: http://arxiv.org/abs/2102.06966v1
• Date: Sat, 13 Feb 2021 17:46:57 GMT
• Title: Graph Convolution for Semi-Supervised Classification: Improved Linear Separability and Out-of-Distribution Generalization
• Authors: Aseem Baranwal, Kimon Fountoulakis, Aukosh Jagannath
• Abstract summary: A new class of learning models has emerged that relies, at its most basic level, on classifying the data after first applying a graph convolution. We show that graph convolution extends the regime in which the data is linearly separable by a factor of roughly $1/sqrtD$.
• Score: 3.308743964406687
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently there has been increased interest in semi-supervised classification in the presence of graphical information. A new class of learning models has emerged that relies, at its most basic level, on classifying the data after first applying a graph convolution. To understand the merits of this approach, we study the classification of a mixture of Gaussians, where the data corresponds to the node attributes of a stochastic block model. We show that graph convolution extends the regime in which the data is linearly separable by a factor of roughly $1/\sqrt{D}$, where $D$ is the expected degree of a node, as compared to the mixture model data on its own. Furthermore, we find that the linear classifier obtained by minimizing the cross-entropy loss after the graph convolution generalizes to out-of-distribution data where the unseen data can have different intra- and inter-class edge probabilities from the training data.

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