ICML 2019oral69 citations

Topological Data Analysis of Decision Boundaries with Application to Model Selection

Karthikeyan Natesan Ramamurthy, Kush Varshney, Krishnan Mody

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.

BibTeX
@InProceedings{pmlr-v97-ramamurthy19a,
  title = 	 {Topological Data Analysis of Decision Boundaries with Application to Model Selection},
  author =       {Ramamurthy, Karthikeyan Natesan and Varshney, Kush and Mody, Krishnan},
  booktitle = 	 {Proceedings of the 36th International Conference on Machine Learning},
  pages = 	 {5351--5360},
  year = 	 {2019},
  editor = 	 {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
  volume = 	 {97},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {09--15 Jun},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v97/ramamurthy19a/ramamurthy19a.pdf},
  url = 	 {https://proceedings.mlr.press/v97/ramamurthy19a.html},
  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.}
}
Topological Data Analysis of Decision Boundaries with Application to Model Selection · ICML 2019