Topological Data Analysis of Decision Boundaries with Application to Model Selection

Karthikeyan Natesan Ramamurthy, Kush Varshney, Krishnan Mody

ICML 2019 pp. 5351-5360

/icml/2019/ramamurthy2019icml-topological/

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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Text

Ramamurthy et al. "Topological Data Analysis of Decision Boundaries with Application to Model Selection." International Conference on Machine Learning, 2019.

Markdown

[Ramamurthy et al. "Topological Data Analysis of Decision Boundaries with Application to Model Selection." International Conference on Machine Learning, 2019.](https://mlanthology.org/icml/2019/ramamurthy2019icml-topological/)

BibTeX

@inproceedings{ramamurthy2019icml-topological,
  title     = {{Topological Data Analysis of Decision Boundaries with Application to Model Selection}},
  author    = {Ramamurthy, Karthikeyan Natesan and Varshney, Kush and Mody, Krishnan},
  booktitle = {International Conference on Machine Learning},
  year      = {2019},
  pages     = {5351-5360},
  volume    = {97},
  url       = {https://mlanthology.org/icml/2019/ramamurthy2019icml-topological/}
}