An Iterative Min-Min Optimization Method for Sparse Bayesian Learning

Yasen Wang, Junlin Li, Zuogong Yue, Ye Yuan
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:50859-50873, 2024.

Abstract

As a well-known machine learning algorithm, sparse Bayesian learning (SBL) can find sparse representations in linearly probabilistic models by imposing a sparsity-promoting prior on model coefficients. However, classical SBL algorithms lack the essential theoretical guarantees of global convergence. To address this issue, we propose an iterative Min-Min optimization method to solve the marginal likelihood function (MLF) of SBL based on the concave-convex procedure. The method can optimize the hyperparameters related to both the prior and noise level analytically at each iteration by re-expressing MLF using auxiliary functions. Particularly, we demonstrate that the method globally converges to a local minimum or saddle point of MLF. With rigorous theoretical guarantees, the proposed novel SBL algorithm outperforms classical ones in finding sparse representations on simulation and real-world examples, ranging from sparse signal recovery to system identification and kernel regression.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-wang24al, title = {An Iterative Min-Min Optimization Method for Sparse {B}ayesian Learning}, author = {Wang, Yasen and Li, Junlin and Yue, Zuogong and Yuan, Ye}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {50859--50873}, 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/wang24al/wang24al.pdf}, url = {https://proceedings.mlr.press/v235/wang24al.html}, abstract = {As a well-known machine learning algorithm, sparse Bayesian learning (SBL) can find sparse representations in linearly probabilistic models by imposing a sparsity-promoting prior on model coefficients. However, classical SBL algorithms lack the essential theoretical guarantees of global convergence. To address this issue, we propose an iterative Min-Min optimization method to solve the marginal likelihood function (MLF) of SBL based on the concave-convex procedure. The method can optimize the hyperparameters related to both the prior and noise level analytically at each iteration by re-expressing MLF using auxiliary functions. Particularly, we demonstrate that the method globally converges to a local minimum or saddle point of MLF. With rigorous theoretical guarantees, the proposed novel SBL algorithm outperforms classical ones in finding sparse representations on simulation and real-world examples, ranging from sparse signal recovery to system identification and kernel regression.} }
Endnote
%0 Conference Paper %T An Iterative Min-Min Optimization Method for Sparse Bayesian Learning %A Yasen Wang %A Junlin Li %A Zuogong Yue %A Ye Yuan %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-wang24al %I PMLR %P 50859--50873 %U https://proceedings.mlr.press/v235/wang24al.html %V 235 %X As a well-known machine learning algorithm, sparse Bayesian learning (SBL) can find sparse representations in linearly probabilistic models by imposing a sparsity-promoting prior on model coefficients. However, classical SBL algorithms lack the essential theoretical guarantees of global convergence. To address this issue, we propose an iterative Min-Min optimization method to solve the marginal likelihood function (MLF) of SBL based on the concave-convex procedure. The method can optimize the hyperparameters related to both the prior and noise level analytically at each iteration by re-expressing MLF using auxiliary functions. Particularly, we demonstrate that the method globally converges to a local minimum or saddle point of MLF. With rigorous theoretical guarantees, the proposed novel SBL algorithm outperforms classical ones in finding sparse representations on simulation and real-world examples, ranging from sparse signal recovery to system identification and kernel regression.
APA
Wang, Y., Li, J., Yue, Z. & Yuan, Y.. (2024). An Iterative Min-Min Optimization Method for Sparse Bayesian Learning. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:50859-50873 Available from https://proceedings.mlr.press/v235/wang24al.html.

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