Enhancing Sufficient Dimension Reduction via Hellinger Correlation

Seungbeom Hong, Ilmun Kim, Jun Song
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:18634-18647, 2024.

Abstract

In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based on conditional independence. Our work is primarily motivated by the recent introduction of the Hellinger correlation as a dependency measure. Utilizing this measure, we have developed a method capable of effectively detecting the dimension reduction subspace, complete with theoretical justification. Through extensive numerical experiments, we demonstrate that our proposed method significantly enhances and outperforms existing SDR methods. This improvement is largely attributed to our proposed method’s deeper understanding of data dependencies and the refinement of existing SDR techniques.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-hong24b, title = {Enhancing Sufficient Dimension Reduction via Hellinger Correlation}, author = {Hong, Seungbeom and Kim, Ilmun and Song, Jun}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {18634--18647}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/hong24b/hong24b.pdf}, url = {https://proceedings.mlr.press/v235/hong24b.html}, abstract = {In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based on conditional independence. Our work is primarily motivated by the recent introduction of the Hellinger correlation as a dependency measure. Utilizing this measure, we have developed a method capable of effectively detecting the dimension reduction subspace, complete with theoretical justification. Through extensive numerical experiments, we demonstrate that our proposed method significantly enhances and outperforms existing SDR methods. This improvement is largely attributed to our proposed method’s deeper understanding of data dependencies and the refinement of existing SDR techniques.} }
Endnote
%0 Conference Paper %T Enhancing Sufficient Dimension Reduction via Hellinger Correlation %A Seungbeom Hong %A Ilmun Kim %A Jun Song %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-hong24b %I PMLR %P 18634--18647 %U https://proceedings.mlr.press/v235/hong24b.html %V 235 %X In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based on conditional independence. Our work is primarily motivated by the recent introduction of the Hellinger correlation as a dependency measure. Utilizing this measure, we have developed a method capable of effectively detecting the dimension reduction subspace, complete with theoretical justification. Through extensive numerical experiments, we demonstrate that our proposed method significantly enhances and outperforms existing SDR methods. This improvement is largely attributed to our proposed method’s deeper understanding of data dependencies and the refinement of existing SDR techniques.
APA
Hong, S., Kim, I. & Song, J.. (2024). Enhancing Sufficient Dimension Reduction via Hellinger Correlation. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:18634-18647 Available from https://proceedings.mlr.press/v235/hong24b.html.

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