# Testing Junta Truncation

arXiv: https://arxiv.org/abs/2308.13992 · HTML: https://mlsanity.com/paper/2308.13992/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2023.

## Built on by (most cited first, 3 of 3)

- [Learning Hard-Constrained Models with One Sample](https://mlsanity.com/paper/2311.03332/) (2023)
- [Smoothed Analysis of Learning from Positive Samples](https://mlsanity.com/paper/2504.10428/) (2025)
- [New Statistical and Computational Results for Learning Junta Distributions](https://mlsanity.com/paper/2505.05819/) (2025)

## Abstract (arXiv)

We consider the basic statistical problem of detecting truncation of the uniform distribution on the Boolean hypercube by juntas. More concretely, we give upper and lower bounds on the problem of distinguishing between i.i.d. sample access to either (a) the uniform distribution over 0,1n, or (b) the uniform distribution over 0,1n conditioned on the satisfying assignments of a k-junta f: 0,1n→0,1. We show that (up to constant factors) min2k + lognchoose k, 2k/2log1/2nchoose k samples suffice for this task and also show that a lognchoose k dependence on sample complexity is unavoidable. Our results suggest that testing junta truncation requires learning the set of relevant variables of the junta.