Correspondence Analysis Using Neural Networks

Hsiang Hsu, Salman Salamatian, Flavio P. Calmon
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:2671-2680, 2019.

Abstract

Correspondence analysis (CA) is a multivariate statistical tool used to visualize and interpret data dependencies. CA has found applications in fields ranging from epidemiology to social sciences. However, current methods used to perform CA do not scale to large, high-dimensional datasets. By re-interpreting the objective in CA using an information-theoretic tool called the principal inertia components, we demonstrate that performing CA is equivalent to solving a functional optimization problem over the space of finite variance functions of two random variable. We show that this optimization problem, in turn, can be efficiently approximated by neural networks. The resulting formulation, called the correspondence analysis neural network (CA-NN), enables CA to be performed at an unprecedented scale. We validate the CA-NN on synthetic data, and demonstrate how it can be used to perform CA on a variety of datasets, including food recipes, wine compositions, and images. Our results outperform traditional methods used in CA, indicating that CA-NN can serve as a new, scalable tool for interpretability and visualization of complex dependencies between random variables.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-hsu19b, title = {Correspondence Analysis Using Neural Networks}, author = {Hsu, Hsiang and Salamatian, Salman and Calmon, Flavio P.}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {2671--2680}, 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/hsu19b/hsu19b.pdf}, url = {https://proceedings.mlr.press/v89/hsu19b.html}, abstract = {Correspondence analysis (CA) is a multivariate statistical tool used to visualize and interpret data dependencies. CA has found applications in fields ranging from epidemiology to social sciences. However, current methods used to perform CA do not scale to large, high-dimensional datasets. By re-interpreting the objective in CA using an information-theoretic tool called the principal inertia components, we demonstrate that performing CA is equivalent to solving a functional optimization problem over the space of finite variance functions of two random variable. We show that this optimization problem, in turn, can be efficiently approximated by neural networks. The resulting formulation, called the correspondence analysis neural network (CA-NN), enables CA to be performed at an unprecedented scale. We validate the CA-NN on synthetic data, and demonstrate how it can be used to perform CA on a variety of datasets, including food recipes, wine compositions, and images. Our results outperform traditional methods used in CA, indicating that CA-NN can serve as a new, scalable tool for interpretability and visualization of complex dependencies between random variables.} }
Endnote
%0 Conference Paper %T Correspondence Analysis Using Neural Networks %A Hsiang Hsu %A Salman Salamatian %A Flavio P. Calmon %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-hsu19b %I PMLR %P 2671--2680 %U https://proceedings.mlr.press/v89/hsu19b.html %V 89 %X Correspondence analysis (CA) is a multivariate statistical tool used to visualize and interpret data dependencies. CA has found applications in fields ranging from epidemiology to social sciences. However, current methods used to perform CA do not scale to large, high-dimensional datasets. By re-interpreting the objective in CA using an information-theoretic tool called the principal inertia components, we demonstrate that performing CA is equivalent to solving a functional optimization problem over the space of finite variance functions of two random variable. We show that this optimization problem, in turn, can be efficiently approximated by neural networks. The resulting formulation, called the correspondence analysis neural network (CA-NN), enables CA to be performed at an unprecedented scale. We validate the CA-NN on synthetic data, and demonstrate how it can be used to perform CA on a variety of datasets, including food recipes, wine compositions, and images. Our results outperform traditional methods used in CA, indicating that CA-NN can serve as a new, scalable tool for interpretability and visualization of complex dependencies between random variables.
APA
Hsu, H., Salamatian, S. & Calmon, F.P.. (2019). Correspondence Analysis Using Neural Networks. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:2671-2680 Available from https://proceedings.mlr.press/v89/hsu19b.html.

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