Structured sparsity regularization is a class of methods, and an area of research in statistical learning theory, that extend and generalize sparsity regularization learning methods.[1] Both sparsity and structured sparsity regularization methods seek to exploit the assumption that the output variable (i.e., response, or dependent variable) to be learned can be described by a reduced number of variables in the input space (i.e., the domain, space of features or explanatory variables). Sparsity regularization methods focus on selecting the input variables that best describe the output. Structured sparsity regularization methods generalize and extend sparsity regularization methods, by allowing for optimal selection over structures like groups or networks of input variables in .[2][3]
Common motivation for the use of structured sparsity methods are model interpretability, high-dimensional learning (where dimensionality of may be higher than the number of observations ), and reduction of computational complexity.[4] Moreover, structured sparsity methods allow to incorporate prior assumptions on the structure of the input variables, such as overlapping groups,[2] non-overlapping groups, and acyclic graphs.[3] Examples of uses of structured sparsity methods include face recognition,[5] magnetic resonance image (MRI) processing,[6] socio-linguistic analysis in natural language processing,[7] and analysis of genetic expression in breast cancer.[8]
^Rosasco, Lorenzo; Poggio, Tomasso (December 2014). A Regularization Tour of Machine Learning, MIT-9.520 Lectures Notes.
^ abCite error: The named reference groupLasso was invoked but never defined (see the help page).
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^Jia, Kui; et al. (2012). "Robust and Practical Face Recognition via Structured Sparsity". In Andrew Fitzgibbon; Svetlana Lazebnik; Pietro Perona; Yoichi Sato; Cordelia Schmid (eds.). Computer Vision – ECCV 2012: 12th European Conference on Computer Vision, Florence, Italy, October 7-13, 2012 Proceedings, Part IV.
^Chen, Chen; et al. (2012). "Compressive Sensing MRI with Wavelet Tree Sparsity". Proceedings of the 26th Annual Conference on Neural Information Processing Systems. Vol. 25. Curran Associates. pp. 1115–1123.
^Eisenstein, Jacob; et al. (2011). "Discovering Sociolinguistic Associations with Structured Sparsity". Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics.
^Jacob, Laurent; et al. (2009). "Group Lasso with Overlap and Graph Lasso". Proceedings of the 26th International Conference on Machine Learning.
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