# Minimax Signal Detection in Sparse Additive Models

arXiv: https://arxiv.org/abs/2304.09398 · HTML: https://mlsanity.com/paper/2304.09398/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 47 references that are in the map.
- First posted on arXiv 19 Apr 2023.

## Builds on (most cited first, 7 of 7)

- [On the Non-asymptotic and Sharp Lower Tail Bounds of Random Variables](https://mlsanity.com/paper/1810.09006/) (2018)
- [Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimension](https://mlsanity.com/paper/2302.05851/) (2023)
- [Minimax Optimal Rates of Estimation in High Dimensional Additive Models: Universal Phase Transition](https://mlsanity.com/paper/1503.02817/) (2015)
- [Minimax rates in sparse, high-dimensional changepoint detection](https://mlsanity.com/paper/1907.10012/) (2019)
- [On Estimation of Lr-Norms in Gaussian White Noise Models](https://mlsanity.com/paper/1710.03863/) (2017)
- [Minimax rates for sparse signal detection under correlation](https://mlsanity.com/paper/2110.12966/) (2021)
- [Sparse Signal Detection in Heteroscedastic Gaussian Sequence Models: Sharp Minimax Rates](https://mlsanity.com/paper/2211.08580/) (2022)

## Abstract (arXiv)

Sparse additive models are an attractive choice in circumstances calling for modelling flexibility in the face of high dimensionality. We study the signal detection problem and establish the minimax separation rate for the detection of a sparse additive signal. Our result is nonasymptotic and applicable to the general case where the univariate component functions belong to a generic reproducing kernel Hilbert space. Unlike the estimation theory, the minimax separation rate reveals a nontrivial interaction between sparsity and the choice of function space. We also investigate adaptation to sparsity and establish an adaptive testing rate for a generic function space; adaptation is possible in some spaces while others impose an unavoidable cost. Finally, adaptation to both sparsity and smoothness is studied in the setting of Sobolev space, and we correct some existing claims in the literature.