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Selecting Diverse Features via Spectral Regularization
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Authors: Abhimanyu Das,Anirban Dasgupta,Ravi Kumar
Where published: NeurIPS 2012 12
Document: PDF DOI
Abstract URL: http://papers.nips.cc/paper/4689-selecting-diverse-features-via-spectral-regularization
We study the problem of diverse feature selection in linear regression: selecting a small subset of diverse features that can predict a given objective. Diversity is useful for several reasons such as interpretability, robustness to noise, etc. We propose several spectral regularizers that capture a notion of diversity of features and show that these are all submodular set functions. These regularizers, when added to the objective function for linear regression, result in approximately submodular functions, which can then be maximized approximately by efficient greedy and local search algorithms, with provable guarantees. We compare our algorithms to traditional greedy and $\ell_1$-regularization schemes and show that we obtain a more diverse set of features that result in the regression problem being stable under perturbations.
Where published: NeurIPS 2012 12
Document: PDF DOI
Abstract URL: http://papers.nips.cc/paper/4689-selecting-diverse-features-via-spectral-regularization
We study the problem of diverse feature selection in linear regression: selecting a small subset of diverse features that can predict a given objective. Diversity is useful for several reasons such as interpretability, robustness to noise, etc. We propose several spectral regularizers that capture a notion of diversity of features and show that these are all submodular set functions. These regularizers, when added to the objective function for linear regression, result in approximately submodular functions, which can then be maximized approximately by efficient greedy and local search algorithms, with provable guarantees. We compare our algorithms to traditional greedy and $\ell_1$-regularization schemes and show that we obtain a more diverse set of features that result in the regression problem being stable under perturbations.
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