Alessandro Epasto

Alessandro Epasto

I am a staff research scientist at Google, New York working in the Algorithms and Optimization team lead by Vahab Mirrokni. I received a Ph.D in computer science from Sapienza University of Rome, where I was advised by Professor Alessandro Panconesi and supported by the Google Europe Ph.D. Fellowship in Algorithms, 2011. I was also a post-doc at the department of computer science of Brown University in Providence (RI), USA where I was advised by Professor Eli Upfal. My research interests include algorithmic problems in machine learning and data mining, in particular in the areas of clustering, privacy and large scale graphs analysis.
Authored Publications
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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)
    Preview abstract 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. View details
    Preview abstract The streaming model of computation is a popular approach for working with large-scale data. In this setting, there is a stream of items and the goal is to compute the desired quantities (usually data statistics) while making a single pass through the stream and using as little space as possible. Motivated by the importance of data privacy, we develop differentially private streaming algorithms under the continual release setting, where the union of outputs of the algorithm at every timestamp must be differentially private. Specifically, we study the fundamental $\ell_p$ $(p\in [0,+\infty))$ frequency moment estimation problem under this setting, and give an $\varepsilon$-DP algorithm that achieves $(1+\eta)$-relative approximation $(\forall \eta\in(0,1))$ with $\mathrm{poly}\log(Tn)$ additive error and uses $\mathrm{poly}\log(Tn)\cdot \max(1, n^{1-2/p})$ space, where $T$ is the length of the stream and $n$ is the size of the universe of elements. Our space is near optimal up to poly-logarithmic factors even in the non-private setting. To obtain our results, we first reduce several primitives under the differentially private continual release model, such as counting distinct elements, heavy hitters and counting low frequency elements, to the simpler, counting/summing problems in the same setting. Based on these primitives, we develop a differentially private continual release level set estimation approach to address the $\ell_p$ frequency moment estimation problem. We also provide a simple extension of our results to the harder sliding window model, where the statistics must be maintained over the past $W$ data items. View details
    Measuring Re-identification Risk
    Travis Dick
    Adel Javanmard
    Josh Karlin
    Andres Munoz Medina
    Gabriel Henrique Nunes
    Peilin Zhong
    SIGMOD(2023)
    Preview abstract Compact user representations (such as embeddings) form the backbone of personalization services. In this work, we present a new theoretical framework to measure re-identification risk in such user representations. Our framework, based on hypothesis testing, formally bounds the probability that an attacker may be able to obtain the identity of a user from their representation. As an application, we show how our framework is general enough to model important real-world applications such as the Chrome's Topics API for interest-based advertising. We complement our theoretical bounds by showing provably good attack algorithms for re-identification that we use to estimate the re-identification risk in the Topics API. We believe this work provides a rigorous and interpretable notion of re-identification risk and a framework to measure it that can be used to inform real-world applications. View details
    Preview abstract 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. View details
    Preview abstract 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. View details
    Scalable Differentially Private Clustering via Hierarchically Separated Trees
    Andres Munoz Medina
    Chris Schwiegelshohn
    David Saulpic
    2022 ACM SIGKDD International Conference on Knowledge Discovery and Data Mining(2022) (to appear)
    Preview abstract We study the private $k$-median and $k$-means clustering problem in $d$ dimensional Euclidean space. By leveraging tree embeddings, we give an efficient and easy to implement algorithm, that is empirically competitive with state of the art non private methods. We prove that our method computes a solution with cost at most $O(d^{3/2}\log n)\cdot OPT + O(k d^2 \log^2 n / \epsilon^2)$, where $\epsilon$ is the privacy guarantee. (The dimension term, $d$, can be replaced with $O(\log k)$ using standard dimension reduction techniques.) Although the worst-case guarantee is worse than that of state of the art private clustering methods, the algorithm we propose is practical, runs in near-linear, $\tilde{O}(nkd)$, time and scales to tens of millions of points. We also show that our method is amenable to parallelization in large-scale distributed computing environments. In particular we show that our private algorithms can be implemented in logarithmic number of MPC rounds in the sublinear memory regime. Finally, we complement our theoretical analysis with an empirical evaluation demonstrating the algorithm's efficiency and accuracy in comparison to other privacy clustering baselines. View details
    Preview abstract The sliding window model of computation captures scenarios in which data is arriving continuously, but only the latest $w$ elements should be used for analysis. The goal is to design algorithms that update the solution efficiently with each arrival rather than recomputing it from scratch. In this work, we focus on $k$-clustering problems such as $k$-means and $k$-median. In this setting, we give simple and practical algorithms that come with stronger performance guarantees than previously known results. Empirically, we show that our methods store only a small fraction of the data, are orders of magnitude faster, and find solutions with cost only slightly worse than those returned by algorithms that have access to the full dataset. View details
    Fair Correlation clustering
    Ravi Kumar
    23rd International Conference on Artificial Intelligence and Statistics (AISTATS 2020)(2020) (to appear)
    Preview abstract In this paper, we study correlation clustering under fairness constraints. Fair variants of k-median and k-center clustering have been studied recently, and approximation algorithms using a notion called fairlet decomposition have been proposed. We obtain approximation algorithms for fair correlation clustering under several important types of fairness constraints. Our results hinge on obtaining a fairlet decomposition for correlation clustering by introducing a novel combinatorial optimization problem. We define a fairlet decomposition with cost similar to the k-median cost and this allows us to obtain approximation algorithms for a wide range of fairness constraints. We complement our theoretical results with an in-depth analysis of our algorithms on real graphs where we show that fair solutions to correlation clustering can be obtained with limited increase in cost compared to the state-of-the-art (unfair) algorithms. View details
    Preview abstract Hierarchical Clustering is an unsupervised data analysis method which has been widely used for decades. Despite its popularity, it had an underdeveloped analytical foundation and to address this, Dasgupta recently introduced an optimization view-point of hierarchical clustering with pair- wise similarity information that spurred a line of work shedding light on old algorithms (e.g., Average-Linkage), but also designing new algorithms. Here, for the maximization dual of Dasgupta’s objec- tive (introduced by Moseley-Wang), we present polynomial-time 42.46% approximation algorithms that use Max-Uncut Bisection as a subroutine. The previous best worst-case approximation factor in polynomial time was 33.6%, improving only slightly over Average-Linkage which achieves 33.3%. Finally, we complement our positive results by providing APX-hardness (even for 0-1 similarities), under the Small Set Expansion hypothesis. View details
    Preview abstract As machine learning has become more and more integrated into our businesses and lifestyles, researchers have begun to recognize the necessity of ensuring machine learning systems are fair. Recently, there has been an interest in defining a notion of fairness that mitigates over-representation in traditional clustering. In this paper we extend this notion to hierarchical clustering, where the goal is to recursively partition the data to optimize a certain objective~\cite{dasgupta}. For various natural objectives, we obtain simple, efficient algorithms to find a provably good fair hierarchical clustering. Empirically, we show that our algorithms can find a fair hierarchical clustering, surprisingly, with only a negligible loss in the objective. View details