Triply Stochastic Gradients on Multiple Kernel Learning

Xiang Li, Bin Gu, Shuang Ao, Huaimin Wang, Charles X. Ling
Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, PMLR R15:829-837, 2017.

Abstract

Multiple Kernel Learning (MKL) is highly useful for learning complex data with multi- ple cues or representations. However, MKL is known to have poor scalability because of the expensive kernel computation. Dai et al (2014) proposed to use a doubly Stochastic Gradient Descent algorithm (doubly SGD) to greatly improve the scalability of kernel meth- ods. However, the algorithm is not suitable for MKL because it cannot learn the kernel weights. In this paper, we provide a novel ex- tension to doubly SGD for MKL so that both the decision functions and the kernel weights can be learned simultaneously. To achieve this, we develop the triply Stochastic Gradient De- scent (triply SGD) algorithm which involves three sources of randomness – the data points, the random features, and the kernels, which was not considered in previous work. We prove that our algorithm enjoys similar conver- gence rate as that of doubly SGD. Comparing to several traditional MKL solutions, we show that our method has faster convergence speed and achieved better accuracy. Most impor- tantly, our method makes it possible to learn MKL problems with millions of data points on a normal desktop PC.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR15-li17a, title = {Triply Stochastic Gradients on Multiple Kernel Learning}, author = {Li, Xiang and Gu, Bin and Ao, Shuang and Wang, Huaimin and Ling, Charles X.}, booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence}, pages = {829--837}, year = {2017}, editor = {Elidan, Gal and Kersting, Kristian}, volume = {R15}, series = {Proceedings of Machine Learning Research}, month = {11--15 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r15/main/assets/li17a/li17a.pdf}, url = {https://proceedings.mlr.press/r15/li17a.html}, abstract = {Multiple Kernel Learning (MKL) is highly useful for learning complex data with multi- ple cues or representations. However, MKL is known to have poor scalability because of the expensive kernel computation. Dai et al (2014) proposed to use a doubly Stochastic Gradient Descent algorithm (doubly SGD) to greatly improve the scalability of kernel meth- ods. However, the algorithm is not suitable for MKL because it cannot learn the kernel weights. In this paper, we provide a novel ex- tension to doubly SGD for MKL so that both the decision functions and the kernel weights can be learned simultaneously. To achieve this, we develop the triply Stochastic Gradient De- scent (triply SGD) algorithm which involves three sources of randomness – the data points, the random features, and the kernels, which was not considered in previous work. We prove that our algorithm enjoys similar conver- gence rate as that of doubly SGD. Comparing to several traditional MKL solutions, we show that our method has faster convergence speed and achieved better accuracy. Most impor- tantly, our method makes it possible to learn MKL problems with millions of data points on a normal desktop PC.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Triply Stochastic Gradients on Multiple Kernel Learning %A Xiang Li %A Bin Gu %A Shuang Ao %A Huaimin Wang %A Charles X. Ling %B Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2017 %E Gal Elidan %E Kristian Kersting %F pmlr-vR15-li17a %I PMLR %P 829--837 %U https://proceedings.mlr.press/r15/li17a.html %V R15 %X Multiple Kernel Learning (MKL) is highly useful for learning complex data with multi- ple cues or representations. However, MKL is known to have poor scalability because of the expensive kernel computation. Dai et al (2014) proposed to use a doubly Stochastic Gradient Descent algorithm (doubly SGD) to greatly improve the scalability of kernel meth- ods. However, the algorithm is not suitable for MKL because it cannot learn the kernel weights. In this paper, we provide a novel ex- tension to doubly SGD for MKL so that both the decision functions and the kernel weights can be learned simultaneously. To achieve this, we develop the triply Stochastic Gradient De- scent (triply SGD) algorithm which involves three sources of randomness – the data points, the random features, and the kernels, which was not considered in previous work. We prove that our algorithm enjoys similar conver- gence rate as that of doubly SGD. Comparing to several traditional MKL solutions, we show that our method has faster convergence speed and achieved better accuracy. Most impor- tantly, our method makes it possible to learn MKL problems with millions of data points on a normal desktop PC. %Z Reissued by PMLR on 04 October 2026.
APA
Li, X., Gu, B., Ao, S., Wang, H. & Ling, C.X.. (2017). Triply Stochastic Gradients on Multiple Kernel Learning. Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R15:829-837 Available from https://proceedings.mlr.press/r15/li17a.html. Reissued by PMLR on 04 October 2026.

Related Material