# Information-Theoretic Bounds for Adaptive Sparse Recovery

arXiv: https://arxiv.org/abs/1402.5731 · HTML: https://mlsanity.com/paper/1402.5731/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2014.

## Built on by (most cited first, 1 of 1)

- [ℝ2k is Theoretically Large Enough for Embedding-based Top-k Retrieval](https://mlsanity.com/paper/2601.20844/) (2026)

## Abstract (arXiv)

We derive an information-theoretic lower bound for sample complexity in sparse recovery problems where inputs can be chosen sequentially and adaptively. This lower bound is in terms of a simple mutual information expression and unifies many different linear and nonlinear observation models. Using this formula we derive bounds for adaptive compressive sensing (CS), group testing and 1-bit CS problems. We show that adaptivity cannot decrease sample complexity in group testing, 1-bit CS and CS with linear sparsity. In contrast, we show there might be mild performance gains for CS in the sublinear regime. Our unified analysis also allows characterization of gains due to adaptivity from a wider perspective on sparse problems.