Recently, under the guidance of Associate Professor Qiu Yixuan from our college, Wang Chenrui, an undergraduate student in the 2021 Statistics Experimental Class, published a paper as the first author at the International Conference on Machine Learning (ICML), a top international conference on machine learning The Sparse-Plus-Low-Rank Quasi-Newton Method for Entropic Regularized Optimal Transport。 ICML is one of the top three international academic conferences in the field of machine learning worldwide (ICML, NeurIPS, and ICLR), representing the highest academic standards and broad influence in the field.
This paper focuses on the classic problem of optimal transmission in statistical machine learning and proposes a new quasi Newton optimization algorithm to address the shortcomings of existing methods, such as slow convergence speed and low computational efficiency. The paper integrates two acceleration frameworks, the Hessian matrix sparsity method and the Broyden Fletcher Goldfarb Shanno quasi Newton method. Firstly, the working mechanism of Hessian matrix sparsity is theoretically analyzed. Then, a low rank compensation term is innovatively introduced to construct a special matrix structure of "sparsity+low rank": this structure can be used to efficiently solve large-scale linear equation systems, thereby replacing the Hessian matrix in classical Newton methods and achieving the goal of improving computational efficiency. The theoretical analysis of the paper indicates that the new algorithm has global convergence and at least linear local convergence speed; Combining various simulations and numerical experiments on real data, this algorithm demonstrates significant performance improvement in large-scale optimal transmission tasks. This research project was launched in September 2024 and completed over a period of 6 months under the careful guidance of Associate Professor Qiu Yixuan.
In recent years, our institute has published multiple research results cultivated through academic top-notch research training programs in top domestic and international journals such as The Annals of Applied Statistics and Journal of Mathematics. These achievements not only reflect the significant achievements in cultivating top-notch talents among our undergraduate students, but also fully demonstrate that our undergraduate students' research capabilities in the forefront of machine learning theory and multimodal learning have reached the international advanced level. In the future, our college will continue to strengthen the undergraduate training model with a solid foundation and broad vision, vigorously support students to participate in various scientific research and innovation projects, and cultivate first-class composite statistical talents.
Contribution | Xiong Jufeng and Wang Chenrui (Student)
Review | Li Tao
