Autoencoding any Data through Kernel Autoencoders

Pierre Laforgue, Stéphan Clémençon, Florence d’Alche-Buc
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:1061-1069, 2019.

Abstract

This paper investigates a novel algorithmic approach to data representation based on kernel methods. Assuming that the observations lie in a Hilbert space X , the introduced Kernel Autoencoder (KAE) is the composition of mappings from vector-valued Reproducing Kernel Hilbert Spaces (vv-RKHSs) that minimizes the expected reconstruction error. Beyond a first extension of the autoencoding scheme to possibly infinite dimensional Hilbert spaces, KAE further allows to autoencode any kind of data by choosing X to be itself a RKHS. A theoretical analysis of the model is carried out, providing a generalization bound, and shedding light on its connection with Kernel Principal Component Analysis. The proposed algorithms are then detailed at length: they crucially rely on the form taken by the minimizers, revealed by a dedicated Representer Theorem. Finally, numerical experiments on both simulated data and real labeled graphs (molecules) provide empirical evidence of the KAE performances.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-laforgue19a, title = {Autoencoding any Data through Kernel Autoencoders}, author = {Laforgue, Pierre and Cl\'{e}men\c{c}on, St\'{e}phan and d'Alche-Buc, Florence}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {1061--1069}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/laforgue19a/laforgue19a.pdf}, url = {https://proceedings.mlr.press/v89/laforgue19a.html}, abstract = {This paper investigates a novel algorithmic approach to data representation based on kernel methods. Assuming that the observations lie in a Hilbert space X , the introduced Kernel Autoencoder (KAE) is the composition of mappings from vector-valued Reproducing Kernel Hilbert Spaces (vv-RKHSs) that minimizes the expected reconstruction error. Beyond a first extension of the autoencoding scheme to possibly infinite dimensional Hilbert spaces, KAE further allows to autoencode any kind of data by choosing X to be itself a RKHS. A theoretical analysis of the model is carried out, providing a generalization bound, and shedding light on its connection with Kernel Principal Component Analysis. The proposed algorithms are then detailed at length: they crucially rely on the form taken by the minimizers, revealed by a dedicated Representer Theorem. Finally, numerical experiments on both simulated data and real labeled graphs (molecules) provide empirical evidence of the KAE performances.} }
Endnote
%0 Conference Paper %T Autoencoding any Data through Kernel Autoencoders %A Pierre Laforgue %A Stéphan Clémençon %A Florence d’Alche-Buc %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-laforgue19a %I PMLR %P 1061--1069 %U https://proceedings.mlr.press/v89/laforgue19a.html %V 89 %X This paper investigates a novel algorithmic approach to data representation based on kernel methods. Assuming that the observations lie in a Hilbert space X , the introduced Kernel Autoencoder (KAE) is the composition of mappings from vector-valued Reproducing Kernel Hilbert Spaces (vv-RKHSs) that minimizes the expected reconstruction error. Beyond a first extension of the autoencoding scheme to possibly infinite dimensional Hilbert spaces, KAE further allows to autoencode any kind of data by choosing X to be itself a RKHS. A theoretical analysis of the model is carried out, providing a generalization bound, and shedding light on its connection with Kernel Principal Component Analysis. The proposed algorithms are then detailed at length: they crucially rely on the form taken by the minimizers, revealed by a dedicated Representer Theorem. Finally, numerical experiments on both simulated data and real labeled graphs (molecules) provide empirical evidence of the KAE performances.
APA
Laforgue, P., Clémençon, S. & d’Alche-Buc, F.. (2019). Autoencoding any Data through Kernel Autoencoders. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:1061-1069 Available from https://proceedings.mlr.press/v89/laforgue19a.html.

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