Badih Ghazi
I am a Research Scientist in the Algorithms & Optimization Team at Google. Here's a link to my personal webpage
Authored Publications
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Differentially Private All-Pairs Shortest Path Distances: Improved Algorithms and Lower Bounds
Jelani Osei Nelson
Justin Y. Chen
Shyam Narayanan
Yinzhan Xu
SODA 2023 (to appear)
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We study the problem of releasing the weights of all-pairs shortest paths in a weighted undirected graph with differential privacy (DP). In this setting, the underlying graph is fixed and two graphs are neighbors if their edge weights differ by at most 1 in the ℓ1-distance. We give an algorithm with additive error ̃O(n^2/3/ε) in the ε-DP case and an algorithm with additive error ̃O(√n/ε) in the (ε, δ)-DP case, where n denotes the number of vertices. This positively answers a question of Sealfon [Sea16, Sea20], who asked whether a o(n) error algorithm exists. We also show that an additive error of Ω(n1/6) is necessary for any sufficiently small ε, δ > 0.
Furthermore, we show that if the graph is promised to have reasonably bounded weights, one can improve the error further to roughly n^{(√17−3)/2+o(1)}/ε in the ε-DP case and roughly n^{√2−1+o(1)}/ε in the (ε, δ)-DP case. Previously, it was only known how to obtain ̃O(n2/3/ε1/3) additive error in the ε-DP case and ̃O(√n/ε) additive error in the (ε, δ)-DP case for bounded-weight graphs [Sea16].
Finally, we consider a relaxation where a multiplicative approximation is allowed. We show that, with a multiplicative approximation factor k, the additive error can be reduced to ̃O(n^{1/2+O(1/k)}/ε) in the ε-DP case and ̃O(n^{1/3+O(1/k)}/ε) in the (ε, δ)-DP case.
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We consider the task of producing heatmaps from users' aggregated data while protecting their privacy. We give a differentially private algorithm for this task and demonstrate its advantages over previous algorithms on several real-world datasets.
Our core algorithmic primitive is a differentially private procedure that takes in a set of distributions and produces an output that is close in Earth Mover's Distance (EMD) to the average of the inputs. We prove theoretical bounds on the error of our algorithm under certain sparsity assumption and that these are essentially optimal.
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Differential privacy is often applied with a privacy parameter that is larger than the theory suggests is ideal; various informal justifications for tolerating large privacy parameters have been proposed.
In this work, we consider partial differential privacy (DP), which allows quantifying the privacy guarantee on a per-attribute basis.
In this framework, we study several basic data analysis and learning tasks, and design algorithms whose per-attribute privacy parameter is smaller that the best possible privacy parameter for the entire record of a person (i.e., all the attributes).
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Leveraging Bias-Variance Trade-offs for Regression with Label Differential Privacy
Ashwinkumar Badanidiyuru Varadaraja
Avinash Varadarajan
Chiyuan Zhang
Ethan Leeman
Pritish Kamath
NeurIPS 2023 (2023)
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We propose a new family of label randomization mechanisms for the task of training regression models under the constraint of label differential privacy (DP). In particular, we leverage the trade-offs between bias and variance to construct better noising mechanisms depending on a privately estimated prior distribution over the labels. We demonstrate that these mechanisms achieve state-of-the-art privacy-accuracy trade-offs on several datasets, highlighting the importance of bias-reducing constraints when training neural networks with label DP. We also provide theoretical results shedding light on the structural properties of the optimal bias-reduced mechanisms.
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In this work, we study the task of estimating the numbers of distinct and k-occurring items in a time window under the constraint of differential privacy (DP). We consider several variants depending on whether the queries are on general time windows (between times t1 and t2), or are restricted to being cumulative (between times 1 and t2), and depending on whether the DP neighboring relation is event-level or the more stringent item-level. We obtain nearly tight upper and lower bounds on the errors of DP algorithms for these problems. En route, we obtain an event-level DP algorithm for estimating, at each time step, the number of distinct items seen over the last W updates with error polylogarithmic in W; this answers an open question of Bolot et al. (ICDT 2013).
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In this paper we consider the problem of aggregating multiple user-generated tracks in a differentially private manner. For this problem we propose a new aggregation algorithm that adds noise sufficient enough to guarantee privacy while preserving the utility of the aggregate. Under natural and simple assumptions, we also show that this algorithm has provably good guarantees.
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We introduce a new algorithm for numerical composition of privacy random variables, useful for computing the accurate privacy parameters for compositions of mechanisms.
For the task of self-composing a broad class of mechanisms $K$ times, this algorithm achieves a running time \& memory usage of $\polylog(K)$ (e.g., this class includes the sub-sampled Gaussian mechanism, that appears in the analysis of DP-SGD).
By comparison, recent work by Gopi et al. (NeurIPS 2021) has a running time of $\wtilde{O}(\sqrt{K})$ for the same task.
Our approach extends to the case of composing $K$ different mechanisms in the same class, improving upon the running time / memory usage in the work of Gopi et al. from $\wtilde{O}(K^{1.5})$ to $\wtilde{O}(K)$.
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In this paper, we consider the problem of differentially private (DP) algorithms for isotonic regression. For the most general problem of isotonic regression over a partially ordered set (poset) X and for any Lipschitz loss function, we obtain a pure-DP algorithm that, given n input points, has an expected excess empirical risk of roughly width(X)⋅log|X|/n, where width(X) is the width of the poset. In contrast, we also obtain a near-matching lower bound of roughly (width(X)+log|X|)/n, that holds even for approximate-DP algorithms. Moreover, we show that the above bounds are essentially the best that can be obtained without utilizing any further structure of the poset.
In the special case of a totally ordered set and for ℓ1 and ℓ2^2 losses, our algorithm can be implemented in near-linear running time; we also provide extensions of this algorithm to the problem of private isotonic regression with additional structural constraints on the output function.
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The privacy loss distribution (PLD) provides a tight characterization of the privacy loss of a mechanism in the context of differential privacy (DP). Recent work has shown that PLD-based accounting allows for tighter (ε,δ)-DP guarantees for many popular mechanisms compared to other known methods. A key question in PLD-based accounting is how to approximate any (potentially continuous) PLD with a PLD over any specified discrete support.
We present a novel approach to this problem. Our approach supports both pessimistic estimation, which overestimates the hockey-stick divergence (i.e., δ) for any value of ε, and optimistic estimation, which underestimates the hockey-stick divergence. Moreover, we show that our pessimistic estimate is the best possible among all pessimistic estimates. Experimental evaluation shows that our approach can work with much larger discretization intervals while keeping a similar error bound compared to previous approaches and yet give a better approximation than existing methods.
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