arXiv subjects

Ria Stevens

Publications and source records attributed to Ria Stevens.

5 recordsLinked to original sources

arXiv2026

Optimal Prediction-Augmented Algorithms for Testing Independence of Distributions

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 \textit{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.

stat.ML↗

arXiv2026

Exploiting Low-Rank Objective Structure in Discrete Quadratic Optimization

We study the problem of maximizing a complex-valued quadratic form over the $K^{\text{th}}$ roots of unity. We show that when the objective matrix $\mathbf{Q}^\star \in \mathbb{C}^{n \times n}$ of the quadratic has rank $r$, the global maximizer belongs to a candidate set of size $O(rn^{2r-1})$. This set can be constructed deterministically in $O(rn^{2r+1})$ time by enumerating the vertices of a hyperplane arrangement in $\mathbb{R}^{2r}.$ The algorithm is embarrassingly parallel; with~$P$ processors, the time complexity drops to $O(r n^{2r+1}/P)$. For approximately low-rank settings, where the objective matrix is a noise-perturbed variant of a rank-$r$ matrix, we prove that applying our framework to a spectral truncation yields a multiplicative $(1 - O(\left\|\mathbf{H}\right\|_2 / \delta^{\star}))$-approximation guarantee, where $\delta^{\star}$ denotes the eigengap of the underlying rank-$r$ matrix and $\mathbf{H}$ represents the perturbation. To scale to high-dimensional problems, we establish a randomized sampling variant. We prove that uniformly sampling $S \geq O(1/\varepsilon^{r-1})$ candidates achieves a $(1-\varepsilon)\cos^2(\pi / K)$-approximation of the optimal rank-$r$ solution with high probability. Crucially, this sample size is entirely independent of $n$, reducing the overall runtime to $O(S \cdot n^2)$. Computational experiments on synthetic benchmarks and large-scale graphs for \textsc{Max-3-Cut} confirm that our algorithms match or exceed semi-definite programming solution quality on structured instances while enabling massive parallelization across heterogeneous hardware and scaling seamlessly to problems where $n \geq 10^6$.

cs.DS↗

arXiv2025

High-Probability Bounds For Heterogeneous Local Differential Privacy

We study statistical estimation under local differential privacy (LDP) when users may hold heterogeneous privacy levels and accuracy must be guaranteed with high probability. Departing from the common in-expectation analyses, and for one-dimensional and multi-dimensional mean estimation problems, we develop finite sample upper bounds in $\ell_2$-norm that hold with probability at least $1-\beta$. We complement these results with matching minimax lower bounds, establishing the optimality (up to constants) of our guarantees in the heterogeneous LDP regime. We further study distribution learning in $\ell_\infty$-distance, designing an algorithm with high-probability guarantees under heterogeneous privacy demands. Our techniques offer principled guidance for designing mechanisms in settings with user-specific privacy levels.

stat.ML↗

arXiv2025

Nearly-Linear Time Private Hypothesis Selection with the Optimal Approximation Factor

Estimating the density of a distribution from its samples is a fundamental problem in statistics. Hypothesis selection addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions -- referred to as 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 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.

cs.DS↗

arXiv2023

CrysFormer: Protein Structure Prediction via 3d Patterson Maps and Partial Structure Attention

Determining the structure of a protein has been a decades-long open question. A protein's three-dimensional structure often poses nontrivial computation costs, when classical simulation algorithms are utilized. Advances in the transformer neural network architecture -- such as AlphaFold2 -- achieve significant improvements for this problem, by learning from a large dataset of sequence information and corresponding protein structures. Yet, such methods only focus on sequence information; other available prior knowledge, such as protein crystallography and partial structure of amino acids, could be potentially utilized. To the best of our knowledge, we propose the first transformer-based model that directly utilizes protein crystallography and partial structure information to predict the electron density maps of proteins. Via two new datasets of peptide fragments (2-residue and 15-residue) , we demonstrate our method, dubbed \texttt{CrysFormer}, can achieve accurate predictions, based on a much smaller dataset size and with reduced computation costs.

cs.LG↗