Topological Data Analysis of Decision Boundaries with Application to Model Selection

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Karthikeyan Natesan Ramamurthy, Kush Varshney, Krishnan Mody ;
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:5351-5360, 2019.

Abstract

We propose the labeled Cech complex, the plain labeled Vietoris-Rips complex, and the locally scaled labeled Vietoris-Rips complex to perform persistent homology inference of decision boundaries in classification tasks. We provide theoretical conditions and analysis for recovering the homology of a decision boundary from samples. Our main objective is quantification of deep neural network complexity to enable matching of datasets to pre-trained models to facilitate the functioning of AI marketplaces; we report results for experiments using MNIST, FashionMNIST, and CIFAR10.

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