Machine learning based on sparsity-inducing regularization for matrices

本课题的研究成果可以概括如下：1.将对偶增广拉格朗日(DAL)算法扩展到处理矩阵的谱正则化问题，提出了M-DAL算法(ICML2010)。DAL和M-DAL算法的超线性收敛被证明并发表在JMLR上。对DAL和相关算法的评论已作为《机器学习的优化》(麻省理工学院出版社)的一部分发表。我还公开了代码，以促进其在更广泛的研究社区中的使用。2.为了处理非数值型数据，我对DAL进行了扩展，使其能够处理数千个核的多核学习。这项研究发表在《机器学习杂志》上。3.将该框架推广到高阶张量的谱正则化，并分析了其统计性能。这是在NIPS2011上提出的。

The outcomes of this research project can be summarized as follows:1. I have extended the dual augmented Lagrangian (DAL) algorithm to deal with spectral regularization for matrices and proposed the M-DAL algorithm(ICML2010). The super-linear convergence of DAL and M-DAL algorithms wasproven and published in JMLR. A review of DAL and related algorithms has beenpublished as part of “Optimization for Machine Learning” (MIT Press). I have alsomade the code publicly available to promote its use in wider research communities. 2. In order to deal with non-numerical data, I have extended DAL to handle multiplekernel learning with thousands of kernels. This was published in MachineLearning Journal. 3. I have extended the framework to spectral regularization for higher-order tensors and analyzed its statistical performance. This was presented at NIPS2011.