針對一次正則化及分組一次正則化問題的隨機活動集近端擬牛頓法

盧昱辰

doi:10.6342/NTU201603353

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針對一次正則化及分組一次正則化問題的隨機活動集近端擬牛頓法

Stochastic Active-Set Proximal Quasi-Newton Method for L1 and Group-L1 Regularized Learning

盧昱辰 , Masters　　Advisor：林守德　　

英文 DOI： 10.6342/NTU201603353

特徵選擇；大規模學習； feature selection ； large-scale learning

Abstract │ Reference (27) │ Altmetrics

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L1 regularization has become one of the standard techniques for feature selection. Furthermore, when structural prior knowledge is available, we can extend the feature selection problem to selecting (predefined) groups of variables, which can be achieved via solving a Lp;1 regularization. To deal with high dimensional learning tasks, shrinking heuristics and greedy method are often exploited to maintain a relatively small working set. However, in practice, shrinking could be too conservative while greedy method could be too expensive in the search of greedy variable. In this work, we propose a Stochastic Active-Set method that maintains an active-set by an approximate and unbiased greedy search method that finds active variables with certain probability suffices to achieve fast convergence. A balance between exploiting active set and exploring high-dimensional space is achieved via a double sampling strategy. In addition, to handle loss function of expensive evaluation cost, we construct a new variant of Quasi-Newton approximation for our Active-Set method, which does not require computation of the whole gradient vector. In our experiments, the proposed algorithm leads to significant speed up over state-of-the-art solvers for L1, L2;1 and Linf;1 regularized problems of computationally expensive loss function.

Reference ( 27 ) 〈TOP〉

[1] G. Andrew and J. Gao. Scalable training of l 1-regularized log-linear models. In Proceedings of the 24th international conference on Machine learning, pages 33–40. ACM, 2007.
[2] F. Bach, R. Jenatton, J. Mairal, and G. Obozinski. Structured sparsity through convex optimization. Statistical Science, pages 450–468, 2012.
[3] A. Beck and M. Teboulle. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM journal on imaging sciences, 2(1):183–202, 2009.
[4] Y.-W. Chang, C.-J. Hsieh, K.-W. Chang, M. Ringgaard, and C.-J. Lin. Training and testing low-degree polynomial data mappings via linear svm. The Journal of Machine Learning Research, 11:1471–1490, 2010.
[5] X. Chen, W. Pan, J. T. Kwok, and J. G. Carbonell. Accelerated gradient method for multi-task sparse learning problem. In 2009 Ninth IEEE International Conference on Data Mining, pages 746–751. IEEE, 2009.

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