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Daniel Alabi

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6 papers

2 author rows

TMLR Journal 2023 Journal Article

Bounded Space Differentially Private Quantiles

Daniel Alabi
Omri Ben-Eliezer
Anamay Chaturvedi

Estimating the quantiles of a large dataset is a fundamental problem in both the streaming algorithms literature and the differential privacy literature. However, all existing private mechanisms for distribution-independent quantile computation require space at least linear in the input size $n$. In this work, we devise a differentially private algorithm for the quantile estimation problem, with strongly sublinear space complexity, in the one-shot and continual observation settings. Our basic mechanism estimates any $\alpha$-approximate quantile of a length-$n$ stream over a data universe $\mathcal{X}$ with probability $1-\beta$ using $O\left( \frac{\log (|\mathcal{X}|/\beta) \log (\alpha \epsilon n)}{\alpha \epsilon} \right)$ space while satisfying $\epsilon$-differential privacy at a single time point. Our approach builds upon deterministic streaming algorithms for non-private quantile estimation instantiating the exponential mechanism using a utility function defined on sketch items, while (privately) sampling from intervals defined by the sketch. We also present another algorithm based on histograms that is especially well-suited to the multiple quantiles case. We implement our algorithms and experimentally evaluate them on synthetic and real-world datasets.

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TMLR Journal 2023 Journal Article

Privacy Budget Tailoring in Private Data Analysis

Daniel Alabi
Chris Wiggins

We consider the problem of learning differentially private linear and logistic regression models that do not exhibit disparate performance for minority groups in the data. Small-sized datasets pose a challenging regime for differential privacy; that is, satisfying differential privacy while learning models from data can lead to models with worse accuracy for minority---in size---subgroups. To address this challenge, inspired by Abowd & Schmutte (2018), we propose: (i) to systematically tailor the privacy budget to the different groups, (ii) use linear optimization oracles in a grid to optimize Lagrangian objectives that correspond to fair learning and optimization. We present efficient differentially private algorithms for linear and logistic regression subject to fairness constraints (e.g., bounded group loss) that allocate the privacy budget based on the private standard error of each subgroup in the data. Consequently, the formulation reduces the amount of noise added to these groups, which leads to more accurate models for such groups. We validate the proposed, group-aware budget allocation, method on synthetic and real-world datasets where we show significant reductions in prediction error for the smallest groups, while still preserving sufficient privacy to protect the minority group from re-identification attacks. In addition, we provide sample complexity lower bounds for our problem formulation.

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STOC Conference 2023 Conference Paper

Privately Estimating a Gaussian: Efficient, Robust, and Optimal

Daniel Alabi
Pravesh K. Kothari
Pranay Tankala
Prayaag Venkat
Fred Zhang

In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP setting, we give an efficient algorithm that estimates an unknown d -dimensional Gaussian distribution up to an arbitrary tiny total variation error using O ( d 2 logκ) samples while tolerating a constant fraction of adversarial outliers. Here, κ is the condition number of the target covariance matrix. The sample bound matches best non-private estimators in the dependence on the dimension (up to a polylogarithmic factor). We prove a new lower bound on differentially private covariance estimation to show that the dependence on the condition number κ in the above sample bound is also tight. Prior to our work, only identifiability results (yielding inefficient super-polynomial time algorithms) were known for the problem. In the approximate DP setting, we give an efficient algorithm to estimate an unknown Gaussian distribution up to an arbitrarily tiny total variation error using O ( d 2 ) samples while tolerating a constant fraction of adversarial outliers. Prior to our work, all efficient approximate DP algorithms incurred a super-quadratic sample cost or were not outlier-robust. For the special case of mean estimation, our algorithm achieves the optimal sample complexity of O ( d ), improving on a O ( d 1.5 ) bound from prior work. Our pure DP algorithm relies on a recursive private preconditioning subroutine that utilizes recent work of Hopkins et al. (STOC 2022) on private mean estimation. Our approximate DP algorithms are based on a substantial upgrade of the method of stabilizing convex relaxations introduced by Kothari et al. (COLT 2022). In particular, we improve on their mechanism by using a new unnormalized entropy regularization and a new and surprisingly simple mechanism for privately releasing covariances.

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NeurIPS Conference 2022 Conference Paper

Hypothesis Testing for Differentially Private Linear Regression

Daniel Alabi
Salil Vadhan

In this work, we design differentially private hypothesis tests for the following problems in the general linear model: testing a linear relationship and testing for the presence of mixtures. The majority of our hypothesis tests are based on differentially private versions of the $F$-statistic for the general linear model framework, which are uniformly most powerful unbiased in the non-private setting. We also present another test for testing mixtures, based on the differentially private nonparametric tests of Couch, Kazan, Shi, Bray, and Groce (CCS 2019), which is especially suited for the small dataset regime. We show that the differentially private $F$-statistic converges to the asymptotic distribution of its non-private counterpart. As a corollary, the statistical power of the differentially private $F$-statistic converges to the statistical power of the non-private $F$-statistic. Through a suite of Monte Carlo based experiments, we show that our tests achieve desired \textit{significance levels} and have a high \textit{power} that approaches the power of the non-private tests as we increase sample sizes or the privacy-loss parameter. We also show when our tests outperform existing methods in the literature.

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AAAI Conference 2022 Conference Paper

Private Rank Aggregation in Central and Local Models

Daniel Alabi
Badih Ghazi
Ravi Kumar
Pasin Manurangsi

In social choice theory, (Kemeny) rank aggregation is a wellstudied problem where the goal is to combine rankings from multiple voters into a single ranking on the same set of items. Since rankings can reveal preferences of voters (which a voter might like to keep private), it is important to aggregate preferences in such a way to preserve privacy. In this work, we present differentially private algorithms for rank aggregation in the pure and approximate settings along with distributionindependent utility upper and lower bounds. In addition to bounds in the central model, we also present utility bounds for the local model of differential privacy.

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JMLR Journal 2018 Journal Article

Learning Certifiably Optimal Rule Lists for Categorical Data

Elaine Angelino
Nicholas Larus-Stone
Daniel Alabi
Margo Seltzer
Cynthia Rudin

We present the design and implementation of a custom discrete optimization technique for building rule lists over a categorical feature space. Our algorithm produces rule lists with optimal training performance, according to the regularized empirical risk, with a certificate of optimality. By leveraging algorithmic bounds, efficient data structures, and computational reuse, we achieve several orders of magnitude speedup in time and a massive reduction of memory consumption. We demonstrate that our approach produces optimal rule lists on practical problems in seconds. Our results indicate that it is possible to construct optimal sparse rule lists that are approximately as accurate as the COMPAS proprietary risk prediction tool on data from Broward County, Florida, but that are completely interpretable. This framework is a novel alternative to CART and other decision tree methods for interpretable modeling. [abs] [ pdf ][ bib ] &copy JMLR 2018. ( edit, beta )

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