Lower bounds on minimax rates for nonparametric regression with additive sparsity and smoothness

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Generalized Sparse Additive Models (2019, methodology): “Our fast rates match the minimax rates under Gaussian data with a least squares loss [Raskutti et al., 2009] and, our slow rates can be seen as an additive generalization of the lasso slow rates [Dalalyan et al., 2017].”
Limits of Estimating Heterogeneous Treatment Effects: Guidelines for Practical Algorithm Design (2018, background): “Theorem 1 says that estimating CATE is as hard as non-parametric regression for functions with additive sparsity (Raskutti et al., 2009; Yang et al., 2015).”
AutoPrognosis: Automated Clinical Prognostic Modeling via Bayesian Optimization with Structured Kernel Learning (2018, background): “number of dimensions in any subspace (Raskutti et al., 2009; Yang et al., 2015).”
Bayesian Nonparametric Causal Inference: Information Rates and Learning Algorithms (2017, unknown): “Now assume that surfaces f0 and f1 have relevant feature dimensions in the sets P0 and P1 , respectively, where |Pω | = pω ≤ d, ω ∈ {0, 1} [41], then I∗ n (F0 P0 ,F1 P1 ) n −2α 0 2α 0 + p 0 ∨ n −2α 1 2α 1 + p 1 , (30)”