Vincent Pierre Cohen-addad
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In modern datasets, where single records can have multiple owners, enforcing user-level differential privacy requires capping each user's total contribution. This "contribution bounding" becomes a significant combinatorial challenge. Existing sequential algorithms for this task are computationally intensive and do not scale to the massive datasets prevalent today. To address this scalability bottleneck, we propose a novel and efficient distributed algorithm. Our approach models the complex ownership structure as a hypergraph, where users are vertices and records are hyperedges. The algorithm proceeds in rounds, allowing users to propose records in parallel. A record is added to the final dataset only if all its owners unanimously agree, thereby ensuring that no user's predefined contribution limit is violated. This method aims to maximize the size of the resulting dataset for high utility while providing a practical, scalable solution for implementing user-level privacy in large, real-world systems.
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In the differentially private partition selection problem (a.k.a. private set union, private key discovery), users hold subsets of items from an unbounded universe. The goal is to output as many items as possible from the union of the users' sets while maintaining user-level differential privacy. Solutions to this problem are a core building block for many privacy-preserving ML applications including vocabulary extraction in a private corpus, computing statistics over categorical data and learning embeddings over user-provided items.
We propose an algorithm for this problem, MaxAdaptiveDegree(MAD), which adaptively reroutes weight from items with weight far above the threshold needed for privacy to items with smaller weight, thereby increasing the probability that less frequent items are output. Our algorithm can be efficiently implemented in massively parallel computation systems allowing scalability to very large datasets. We prove that our algorithm stochastically dominates the standard parallel algorithm for this problem. We also develop a two-round version of our algorithm, MAD2R, where results of the computation in the first round are used to bias the weighting in the second round to maximize the number of items output. In experiments, our algorithms provide the best results across the board among parallel algorithms and scale to datasets with hundreds of billions of items, up to three orders of magnitude larger than those analyzed by prior sequential algorithms.
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Scalable Private Partition Selection via Adaptive Weighting
Justin Y. Chen
Forty-second International Conference on Machine Learning (2025)
Preview abstract
In the differentially private partition selection problem (a.k.a. private set union, private key discovery), users hold subsets of items from an unbounded universe. The goal is to output as many items as possible from the union of the users' sets while maintaining user-level differential privacy. Solutions to this problem are a core building block for many privacy-preserving ML applications including vocabulary extraction in a private corpus, computing statistics over categorical data and learning embeddings over user-provided items.
We propose an algorithm for this problem, MaxAdaptiveDegree(MAD), which adaptively reroutes weight from items with weight far above the threshold needed for privacy to items with smaller weight, thereby increasing the probability that less frequent items are output. Our algorithm can be efficiently implemented in massively parallel computation systems allowing scalability to very large datasets. We prove that our algorithm stochastically dominates the standard parallel algorithm for this problem. We also develop a two-round version of our algorithm, MAD2R, where results of the computation in the first round are used to bias the weighting in the second round to maximize the number of items output. In experiments, our algorithms provide the best results across the board among parallel algorithms and scale to datasets with hundreds of billions of items, up to three orders of magnitude larger than those analyzed by prior sequential algorithms.
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In the differentially private set union problem, users contribute sets of items as input, and the output is a subset of the union of all items. Algorithms for this problem seek to output as many items as possible while maintaining differential privacy with respect to the addition or removal of an individual user.
The basic solution to this problem maintains a weight over each item. Each user contributes uniformly to the items in their set, random noise is added to the weights, and items with noisy weight above a certain threshold are output. The only scalable (i.e., distributed) algorithms for this problem from prior work are this basic algorithm and an iterative method which repeatedly calls the basic algorithm, ignoring items found in prior invocations.
In this work, we give an improved weighting algorithm over basic uniform weighting. Our algorithm reroutes weight from items with weight far above the threshold to items with smaller weight, thereby increasing the probability that less frequent items are output. The algorithm is scalable and does not suffer any privacy loss when compared to the basic algorithm. We prove that our algorithm will never underperform the basic algorithm and show experimentally that replacing the basic algorithm with ours yields the best results among scalable algorithms for the private set union problem.
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Scalable Private Partition Selection via Adaptive Weighting
Justin Y. Chen
Forty-second International Conference on Machine Learning (2025)
Preview abstract
In the differentially private partition selection problem (a.k.a. private set union, private key discovery), users hold subsets of items from an unbounded universe. The goal is to output as many items as possible from the union of the users' sets while maintaining user-level differential privacy. Solutions to this problem are a core building block for many privacy-preserving ML applications including vocabulary extraction in a private corpus, computing statistics over categorical data and learning embeddings over user-provided items.
We propose an algorithm for this problem, MaxAdaptiveDegree(MAD), which adaptively reroutes weight from items with weight far above the threshold needed for privacy to items with smaller weight, thereby increasing the probability that less frequent items are output. Our algorithm can be efficiently implemented in massively parallel computation systems allowing scalability to very large datasets. We prove that our algorithm stochastically dominates the standard parallel algorithm for this problem. We also develop a two-round version of our algorithm, MAD2R, where results of the computation in the first round are used to bias the weighting in the second round to maximize the number of items output. In experiments, our algorithms provide the best results across the board among parallel algorithms and scale to datasets with hundreds of billions of items, up to three orders of magnitude larger than those analyzed by prior sequential algorithms.
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We consider the classic Euclidean k-median and k-means objective on insertion-only streams,
where the goal is to maintain a (1 + ε)-approximation to the k-median or k-means, while using
as little memory as possible. Over the last 20 years, clustering in data streams has received a
tremendous amount of attention and has been the test-bed for a large variety of new techniques,
including coresets, merge-and-reduce, bicriteria approximation, sensitivity sampling, etc. Despite
this intense effort to obtain smaller and smaller sketches for these problems, all known techniques
require storing at least Ω(log (n∆)) words of memory, where n is size of the input and ∆ is
the aspect ratio. In this paper, we show how to finally bypass this bound and obtain the first
algorithm that achieves a (1 + ε)-approximation to the more general (k, z)-clustering problem,
using only ̃O ( dk / ε^2) · (2^{z log z} ) · min ( 1/ε^z , k) · poly(log log(n∆)) words of memory.
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Private estimation algorithms for stochastic block models and mixture models
Hongjie Chen
Tommaso D'Orsi
Jacob Imola
David Steurer
Stefan Tiegel
54rd Annual ACM Symposium on Theory of Computing (STOC'23) (2023)
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We introduce general tools for designing efficient private estimation algorithms, in the high-dimensional settings, whose statistical guarantees almost match those of the best known non-private algorithms. To illustrate our techniques, we consider two problems: recovery of stochastic block models and learning mixtures of spherical Gaussians. For the former, we present the first efficient (ϵ,δ)-differentially private algorithm for both weak recovery and exact recovery. Previously known algorithms achieving comparable guarantees required quasi-polynomial time. For the latter, we design an (ϵ,δ)-differentially private algorithm that recovers the centers of the k-mixture when the minimum separation is at least O(k^{1/t}/√t). For all choices of t, this algorithm requires sample complexity n≥k^O(1)d^O(t) and time complexity (nd)^O(t). Prior work required minimum separation at least O(√k) as well as an explicit upper bound on the Euclidean norm of the centers.
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We study the fine-grained complexity of the famous $k$-center problem in the metric induced by a graph with $n$ vertices and $m$ edges. The problem is NP-hard to approximate within a factor strictly better than $2$, and several $2$-approximation algorithms are known.
Two of the most well-known approaches for the $2$-approximation are (1) finding a maximal distance $r$-independent set (where the minimum pairwise distance is greater than $r$) and (2) Gonzalez's algorithm that iteratively adds the center farthest from the currently chosen centers.
For the approach based on distance-$r$ independent sets, Thorup [SIAM J. Comput. '05] already gave a nearly linear time algorithm. While Thorup's algorithm is not complicated, it still requires tools such as an approximate oracle for neighborhood size by Cohen [J. Comput. Syst. Sci. '97]. Our main result is a nearly straightforward algorithm that improves the running time by an $O(\log n$) factor. It results in an $(2+\eps)$-approximation for $k$-center in $O((m + n \log n)\log n \log(n/\eps))$ time.
For Gonzalez's algorithm [Theor. Comput. Sci. 85], we show that the simple $\widetilde{O}(mk)$-time implementation is nearly optimal if we insist the {\em exact} implementation. On the other hand, we show that an $(1+\eps)$-approximate version of the algorithm is efficiently implementable, leading to an $(2+\eps)$-approximation algorithm in running time $O((m + n \log n)\log^2 n / \eps)$. We also show that, unlike in the distance $r$-independent set-based algorithm, the dependency of $1/\eps$ in the running time is essentially optimal for $(1 + \eps)$-approximate Gonzalez's.
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We consider the classic correlation clustering problem: Given a complete graphs where edges are
labelled either + or -, the goal is to find a partition of the vertices that minimizes the number of the +
edges across parts plus the number of the - edges within parts.
Recently, Cohen-Addad, Lee and Newman [FOCS’22] showed the first 1.995-approximation for the
problem using the Sherali-Adams hierarchy hence breaking through the integrality gap of 2 of the clas-
sic linear program and improving upon the 2.06-approximation of Chawla, Makarychev, Schramm and
Yaroslavtsev [STOC’15].
We significantly improve the result by providing a 1.73-approximation for the problem, making a
significant step below 2. Our approach brings together a new preprocessing of correlation clustering
instances that enables a new LP formulation which combined with the approach of Cohen-Addad, Lee
and Newman [FOCS’22] and a new rounding method yields the improved bound.
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Consider an agent (say a robot) exploring an unknown graph in search
of some goal state. As it walks around the graph, it learns the
nodes and their neighbors. The agent only knows where the goal state
is when it reaches it. How do we reach this goal while moving only a
small distance? This problem seems hopeless, even on trees of
bounded degree, unless we give the agent some help. In our case,
this help comes in the form of *predictions*: each node $v$
provides a prediction $f(v)$ of its distance to the goal
vertex. Naturally if the predictions are correct, we can reach the
goal quickly. What if some of the predictions are erroneous? This
naturally models graph search problems where we are given some
quality function to guide us towards the goal: in our framework the
quality is given by the distance predictions.
In this work, we initiate a study of this problem with
predictions. We consider the problem on trees (where the problem is
already non-trivial) and give deterministic realgorithms whose
movement cost is only $O(OPT + ERR)$, where $OPT$ is the distance
from the start to the goal vertex, and the $ERR$ is the total number
of vertices whose predictions are erroneous. We also consider a
``planning'' version of the problem where the graph and predictions
are known at the beginning, so the agent can use this global
information to quickly reach the goal. For the planning version, we
give a different algorithm for trees, and then an algorithm for all
(weighted) graphs with bounded doubling dimension.
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