Selective inference for group-sparse linear models

Part of Advances in Neural Information Processing Systems 29 (NIPS 2016)

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Fan Yang, Rina Foygel Barber, Prateek Jain, John Lafferty


We develop tools for selective inference in the setting of group sparsity, including the construction of confidence intervals and p-values for testing selected groups of variables. Our main technical result gives the precise distribution of the magnitude of the projection of the data onto a given subspace, and enables us to develop inference procedures for a broad class of group-sparse selection methods, including the group lasso, iterative hard thresholding, and forward stepwise regression. We give numerical results to illustrate these tools on simulated data and on health record data.