Topological Data Analysis of Decision Boundaries with Application to Model Selection

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Topological Data Analysis of Decision Boundaries with Application to Model Selection %A Karthikeyan Natesan Ramamurthy %A Kush Varshney %A Krishnan Mody %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-ramamurthy19a %I PMLR %P 5351--5360 %U https://proceedings.mlr.press/v97/ramamurthy19a.html %V 97 %X 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.
APA
Ramamurthy, K.N., Varshney, K. & Mody, K.. (2019). Topological Data Analysis of Decision Boundaries with Application to Model Selection. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:5351-5360 Available from https://proceedings.mlr.press/v97/ramamurthy19a.html.

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