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.

Computer Science (CS) faculty recently reviewed and updated curriculum in the CS track at Rice University's summer ''anti-remedial'' bridge program to better align with introductory courses. The goals of the program are to (1) provide students from under-resourced secondary schools the support needed to persist, thrive, and graduate at the same rate as their peers and (2) ensure that these students achieve their academic and professional aspirations. Preliminary results show that anti-remedial programming coupled with advising and peer support increase student grades and identity which are shown to increase sense of belonging (and retention) in STEM.

Estimating the density of a distribution from its samples is a fundamental problem in statistics. \emph{Hypothesis selection} addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions---referred to as \emph{hypotheses}---and the goal is to determine which one best describes the underlying data distribution. This problem is known to be solvable very efficiently, requiring roughly $O(\log n)$ samples and running in $\tilde{O}(n)$ time. The quality of the output is measured via the total variation distance to the unknown distribution, and the approximation factor of the algorithm determines how large this distance is compared to the optimal distance achieved by the best candidate hypothesis. It is known that $\alpha = 3$ is the optimal approximation factor for this problem. We study hypothesis selection under the constraint of \emph{differential privacy}. We propose a differentially private algorithm in the central model that runs in nearly linear time with respect to the number of hypotheses, achieves the optimal approximation factor, and incurs only a modest increase in sample complexity, which remains polylogarithmic in $n$. This resolves an open question posed by [Bun, Kamath, Steinke, Wu, NeurIPS 2019]. Prior to our work, existing upper bounds required quadratic time.