Copula-Nested Spectral Kernel Network

Jinyue Tian, Hui Xue, Yanfang Xue, Pengfei Fang
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:48280-48294, 2024.

Abstract

Spectral Kernel Networks (SKNs) emerge as a promising approach in machine learning, melding solid theoretical foundations of spectral kernels with the representation power of hierarchical architectures. At its core, the spectral density function plays a pivotal role by revealing essential patterns in data distributions, thereby offering deep insights into the underlying framework in real-world tasks. Nevertheless, prevailing designs of spectral density often overlook the intricate interactions within data structures. This phenomenon consequently neglects expanses of the hypothesis space, thus curtailing the performance of SKNs. This paper addresses the issues through a novel approach, the Copula-Nested Spectral Kernel Network (CokeNet). Concretely, we first redefine the spectral density with the form of copulas to enhance the diversity of spectral densities. Next, the specific expression of the copula module is designed to allow the excavation of complex dependence structures. Finally, the unified kernel network is proposed by integrating the corresponding spectral kernel and the copula module. Through rigorous theoretical analysis and experimental verification, CokeNet demonstrates superior performance and significant advancements over SOTA algorithms in the field.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-tian24f, title = {Copula-Nested Spectral Kernel Network}, author = {Tian, Jinyue and Xue, Hui and Xue, Yanfang and Fang, Pengfei}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {48280--48294}, 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/tian24f/tian24f.pdf}, url = {https://proceedings.mlr.press/v235/tian24f.html}, abstract = {Spectral Kernel Networks (SKNs) emerge as a promising approach in machine learning, melding solid theoretical foundations of spectral kernels with the representation power of hierarchical architectures. At its core, the spectral density function plays a pivotal role by revealing essential patterns in data distributions, thereby offering deep insights into the underlying framework in real-world tasks. Nevertheless, prevailing designs of spectral density often overlook the intricate interactions within data structures. This phenomenon consequently neglects expanses of the hypothesis space, thus curtailing the performance of SKNs. This paper addresses the issues through a novel approach, the Copula-Nested Spectral Kernel Network (CokeNet). Concretely, we first redefine the spectral density with the form of copulas to enhance the diversity of spectral densities. Next, the specific expression of the copula module is designed to allow the excavation of complex dependence structures. Finally, the unified kernel network is proposed by integrating the corresponding spectral kernel and the copula module. Through rigorous theoretical analysis and experimental verification, CokeNet demonstrates superior performance and significant advancements over SOTA algorithms in the field.} }
Endnote
%0 Conference Paper %T Copula-Nested Spectral Kernel Network %A Jinyue Tian %A Hui Xue %A Yanfang Xue %A Pengfei Fang %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-tian24f %I PMLR %P 48280--48294 %U https://proceedings.mlr.press/v235/tian24f.html %V 235 %X Spectral Kernel Networks (SKNs) emerge as a promising approach in machine learning, melding solid theoretical foundations of spectral kernels with the representation power of hierarchical architectures. At its core, the spectral density function plays a pivotal role by revealing essential patterns in data distributions, thereby offering deep insights into the underlying framework in real-world tasks. Nevertheless, prevailing designs of spectral density often overlook the intricate interactions within data structures. This phenomenon consequently neglects expanses of the hypothesis space, thus curtailing the performance of SKNs. This paper addresses the issues through a novel approach, the Copula-Nested Spectral Kernel Network (CokeNet). Concretely, we first redefine the spectral density with the form of copulas to enhance the diversity of spectral densities. Next, the specific expression of the copula module is designed to allow the excavation of complex dependence structures. Finally, the unified kernel network is proposed by integrating the corresponding spectral kernel and the copula module. Through rigorous theoretical analysis and experimental verification, CokeNet demonstrates superior performance and significant advancements over SOTA algorithms in the field.
APA
Tian, J., Xue, H., Xue, Y. & Fang, P.. (2024). Copula-Nested Spectral Kernel Network. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:48280-48294 Available from https://proceedings.mlr.press/v235/tian24f.html.

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