Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all product distributions in total variation distance. In the non-parametric finite-sample regime, this task is notoriously expensive, as the minimax sample complexity scales polynomially with the support size. In this work, we move beyond these worst-case limitations by leveraging the framework of augmented distribution testing. We design independence testers that incorporate auxiliary, but potentially untrustworthy, predictive information. Our framework ensures that the tester remains robust, maintaining worst-case validity regardless of the prediction’s quality, while significantly improving sample efficiency when the prediction is accurate. Our main contributions include: (i) a bivariate independence tester for discrete distributions that adaptively reduces sample complexity based on the prediction error; (ii) a generalization to the high-dimensional multivariate setting for testing the independence of $d$ random variables; and (iii) matching minimax lower bounds demonstrating that our testers achieve optimal sample complexity.

An emerging application of wireless sensing is locating and tracking humans in their living environments, a primitive that can be leveraged in both daily life applications and emergency situations. However, most proposed methods have limited spatial resolution when multiple humans are in close vicinity. The problem becomes exacerbated when there is no line-of-sight path to the humans. In this paper, we consider multi-person localization of humans in close vicinity of each other. We propose the use of synthetic aperture radar that combines both translation and rotation to increase effective aperture size, leveraging small rhythmic changes in the radar range due to human breathing. We experimentally evaluate the proposed algorithm in both line-of-sight and through-wall cases with three to five humans in the scene. Our experimental results show that: (i) larger synthetic apertures due to radar translation improve multi-person localization, e.g., by 1.42× when the aperture size is increased by a factor of 2×, and (ii) rotation can largely compensate for gains provided by translation, e.g., rotating the radar over 360° without changing the aperture size results in 1.22× gains over no rotation. Overall, maximal gains of 2.19× are achieved by rotating and translating over a 2× larger aperture.