ICML 2022spotlight1 citations
Measuring dissimilarity with diffeomorphism invariance
Théophile Cantelobre, Carlo Ciliberto, Benjamin Guedj, Alessandro Rudi
Abstract
Measures of similarity (or dissimilarity) are a key ingredient to many machine learning algorithms. We introduce DID, a pairwise dissimilarity measure applicable to a wide range of data spaces, which leverages the data’s internal structure to be invariant to diffeomorphisms. We prove that DID enjoys properties which make it relevant for theoretical study and practical use. By representing each datum as a function, DID is defined as the solution to an optimization problem in a Reproducing Kernel Hilbert Space and can be expressed in closed-form. In practice, it can be efficiently approximated via Nystr{ö}m sampling. Empirical experiments support the merits of DID.
BibTeX
@InProceedings{pmlr-v162-cantelobre22a,
title = {Measuring dissimilarity with diffeomorphism invariance},
author = {Cantelobre, Th{\'e}ophile and Ciliberto, Carlo and Guedj, Benjamin and Rudi, Alessandro},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {2572--2596},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/cantelobre22a/cantelobre22a.pdf},
url = {https://proceedings.mlr.press/v162/cantelobre22a.html},
abstract = {Measures of similarity (or dissimilarity) are a key ingredient to many machine learning algorithms. We introduce DID, a pairwise dissimilarity measure applicable to a wide range of data spaces, which leverages the data’s internal structure to be invariant to diffeomorphisms. We prove that DID enjoys properties which make it relevant for theoretical study and practical use. By representing each datum as a function, DID is defined as the solution to an optimization problem in a Reproducing Kernel Hilbert Space and can be expressed in closed-form. In practice, it can be efficiently approximated via Nystr{ö}m sampling. Empirical experiments support the merits of DID.}
}