# Peilin Zhong

Peilin Zhong is a research scientist at Google NYC in the Algorithms and Optimization team lead by Vahab Mirrokni. He received his Ph.D. from Columbia University (Under supervision of Alex Andoni, Cliff Stein, and Mihalis Yannakakis). Previously, he was an undergraduate student at Institute for Interdisciplinary Information Sciences (Yao Class), Tsinghua University. He has broad interests in theoretical computer science, mainly in design and analysis of algorithms. Some particular interests include parallel and massively parallel algorithms, private algorithms, sketching, streaming algorithms, graph algorithms, machine learning, high dimensional geometry, metric embedding, numerical linear algebra, clustering, and other algorithms related to large-scale data computation.

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Near-Optimal Private and Scalable k-Clustering

Shyam Narayanan

NeurIPS 2022 (2022)

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We study the differentially private (DP) $k$-means and $k$-median clustering problems of $n$ points in $d$-dimensional Euclidean space in the massively parallel computation (MPC) model. We provide two near-optimal algorithms where the near-optimality is in three aspects: they both achieve (1). $O(1)$ parallel computation rounds, (2). near-linear in $n$ and polynomial in $k$ total computational work (i.e., near-linear running time in the sequential setting), (3). $O(1)$ relative approximation and $\text{poly}(k, d)$ additive error, where $\Omega(1)$ relative approximation is provably necessary even for any polynomial-time non-private algorithm, and $\Omega(k)$ additive error is a provable lower bound for any polynomial-time DP $k$-means/median algorithm. Our two algorithms provide a tradeoff between the relative approximation and the additive error: the first has $O(1)$ relative approximation and $\sim (k^{2.5} + k^{1.01} \sqrt{d})$ additive error, and the second one achieves $(1+\gamma)$ relative approximation to the optimal non-private algorithm for an arbitrary small constant $\gamma>0$ and with $\text{poly}(k, d)$ additive error for a larger polynomial dependence on $k$ and $d$.
To achieve our result, we develop a general framework which partitions the data and reduces the DP clustering problem for the entire dataset to the DP clustering problem for each part. To control the blow-up of the additive error introduced by each part, we develop a novel charging argument which might be of independent interest.
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Stars: Tera-Scale Graph Building for Clustering and Learning

Warren Schudy

NeurIPS 2022 (2022)

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A fundamental procedure in the analysis of massive datasets is the construction of similarity graphs. Such graphs play a key role for many downstream tasks, including clustering, classification, graph learning, and nearest neighbor search. For these tasks, it is critical to build graphs which are sparse yet still representative of the underlying data. The benefits of sparsity are twofold: firstly, constructing dense graphs is infeasible in practice for large datasets, and secondly, the runtime of downstream tasks is directly controlled by the sparsity of the similarity graph. In this work, we present Stars: a highly scalable method for building extremely sparse graphs via two-hop spanners, which are graphs where similar points are connected by a path of length at most two. Stars can construct two-hop spanners with significantly fewer similarity comparisons, which are a major bottleneck for learning based models where comparisons are expensive to evaluate. Theoretically, we demonstrate that Stars builds a graph in nearly-linear time, where approximate nearest neighbors are contained within two-hop neighborhoods. To complement our results, we have deployed Stars for multiple data sets allowing for graph building at the Tera-Scale, i.e., for graphs with hundreds of billions of nodes and tens of trillions of edges. We evaluate the performance of Stars for clustering and graph learning, and demonstrate 10~1000-fold improvements in pairwise similarity comparisons and significant improvements in runtime with negligible quality loss.
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Differentially Private Graph Learning via Sensitivity-Bounded Personalized PageRank

Advances in Neural Information Processing Systems (2022)

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Personalized PageRank (PPR) is a fundamental tool in unsupervised learning of graph representations such as node ranking, labeling, and graph embedding. However, while data privacy is one of the most important recent concerns, existing PPR algorithms are not designed to protect user privacy. PPR is highly sensitive to the input graph edges: the difference of only one edge may cause a big change in the PPR vector, potentially leaking private user data.
In this work, we propose an algorithm which outputs an approximate PPR and has provably bounded sensitivity to input edges. In addition, we prove that our algorithm achieves similar accuracy to non-private algorithms when the input graph has large degrees. Our sensitivity-bounded PPR directly implies private algorithms for several tools of graph learning, such as, differentially private (DP) PPR ranking, DP node classification, and DP node embedding. To complement our theoretical analysis, we also empirically verify the practical performances of our algorithms.
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