Current literature typically assumes that the tasks are diverse, i.e., their parameters uniformly span the

We thank all the reviewers for the helpful comments. Here, we address the main concerns raised by the reviewers. While the traditional method (e.g., Lasso) can find important individual The motivations and application are discussed in [1.1.] When the sparse assumption doesn't hold] Theoretically, the sparsity assumption is commonly Motivations] The motivations and one real application where sparsity holds are discussed in [1.1.]

Recently, Sur and Candès [2019] showed that these issues can be corrected by applying a new approximation of the MLE's sampling distribution in this highdimensional regime. Unfortunately, these corrections are difficult to implement in practice, because they require an estimate of thesignal strength, which is a function of the underlying parametersβ of the logistic regression.

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