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Learning discriminative node representations benefits various downstream tasks in graph analysis such as community detection and node classification. Existing graph representation learning methods (e.g., based on random walk and contrastive learning) are limited to maximizing the local similarity of connected nodes. Such pair-wise learning schemes could fail to capture the global distribution of representations, since it has no explicit constraints on the global geometric properties of representation space. To this end, we propose Geometric Graph Representation Learning (G2R) to learn node representations in an unsupervised manner via maximizing rate reduction. In this way, G2R maps nodes in distinct groups (implicitly stored in the adjacency matrix) into different subspaces, while each subspace is compact and different subspaces are dispersedly distributed. G2R adopts a graph neural network as the encoder and maximizes the rate reduction with the adjacency matrix. Furthermore, we theoretically and empirically demonstrate that rate reduction maximization is equivalent to maximizing the principal angles between different subspaces. Experiments on real-world datasets show that G2R outperforms various baselines on node classification and community detection tasks.
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Equi-explanation Maps: Concise and Informative Global Summary Explanations
We propose equi-explanation maps to study the variation in model logic across the input space. These global model-agnostic structures partition the hyper-space of explanation features into regions of similar model logic. Equi-explanation maps act as a concise summary of instance explanations and can provide laymen an at-a-glance understanding of the basis on which the classifier makes its decisions. We thus propose the task of generating $$\epsilon$$-equi-explanation maps, a partitioning of the input space into subspaces such that the standard deviation of explanation vectors in a subspace do not exceed $$\epsilon$$. We adapt existing local and subspace explainability techniques like LIME and MUSE to generate equi-explanation maps on two binary classification datasets using four classification models and evaluate the quality of their partitioning. We find that these techniques produce a sub-optimal number of subspaces (making the maps harder to interpret) and have a considerable run time. We then propose E-map, a new divide-and-conquer based algorithm to produce $$\epsilon$$-equi-explanation maps. E-map is able to decrease the number of subspaces (and hence increase interpretability) and running time as compared to the previous systems for a fixed value of $$\epsilon$$. Finally, given a classifier decision boundary, we try to determine what would be an optimal value for the parameter $$\epsilon$$. We believe good explanation representation methods can increase the trustworthiness and understanding of machine learning models for critical real world tasks.
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- PAR ID:
- 10357768
- Date Published:
- Journal Name:
- Proceedings of the 2022 ACM FAccT* Conference
- Page Range / eLocation ID:
- 464 to 472
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3531146.3533112
