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.

Clarity/Presentation/Related work/Presentation of contribution(s): The paper is overall clearly and well written. Also, the paper is well structured and makes a good introduction to the problem at hand, exposing what the new challenges and the resulting contributions are (e.g., paragraph lines 103-115). At some few places (see details below), some additional details would be useful. Technical level: The paper appears as technically sound and Lemma 1/Theorem 1 represent a non-trivial contribution. Some questions related to the proofs (see afterwards) should be clarified. Experiments: The experimental section may appear as a bit disappointing.

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. Papers published at the Neural Information Processing Systems Conference.