# Active Regression for Single-Index Models with Unknown Link Functions

arXiv: https://arxiv.org/abs/2608.01287 · HTML: https://mlsanity.com/paper/2608.01287/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 13 references that are in the map.
- First posted on arXiv 2 Aug 2026.

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

- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [L1 Regression with Lewis Weights Subsampling](https://mlsanity.com/paper/2105.09433/) (2021)
- [Active Learning for Single Neuron Models with Lipschitz Non-Linearities](https://mlsanity.com/paper/2210.13601/) (2022)
- [Agnostic Active Learning of Single Index Models with Linear Sample Complexity](https://mlsanity.com/paper/2405.09312/) (2024)
- [On computing approximate Lewis weights](https://mlsanity.com/paper/2404.02881/) (2024)
- [One-shot Active Learning Based on Lewis Weight Sampling for Multiple Deep Models](https://mlsanity.com/paper/2405.14121/) (2024)
- [Near-optimal Active Regression of Single-Index Models](https://mlsanity.com/paper/2502.18213/) (2025)

## Abstract (arXiv)

This paper studies active regression for single-index models under general ℓp-loss with an unknown 1-Lipschitz link function f, formulated as minf,x |f(Ax)-b|pp with full access to A but coordinate-query access to b. Prior work established upper bounds for known link functions for all p≥ 1 and for unknown link functions only in the p=2 case, together with lower bounds for p≤ 2. This work addresses the more challenging setting of unknown link functions and general p ≥ 1. A non-adaptive sampling algorithm is presented that achieves a (1+ε)-approximation using O(dp/2vee 1/εpvee 2operatornamepolylog(n/ε)) queries. Nearly tight lower bounds are also established for p>2. These results close much of the remaining gap in active ℓp-regression for single-index models.