Edith Cohen
I am a Research Scientist at Google (Mountain View, CA) since 2015. I am also a (visiting) full professor at the School of Computer Science at Tel Aviv University in Israel. I attended
Tel Aviv University
(Israel)
for my undergraduate studies in math, physics, and
computer science, graduating in 1985, and continued to obtain an M.Sc.
in computer science in 1986, supervised by Michael Tarsi. I then headed to
Stanford, CA, where I
worked on a Ph.D. in Computer
Science,
with
Andrew Goldberg and Nimrod Megiddo, graduating in 1991.
From 1991 to 2012, I was a member of the research staff, first at the
legendary AT&T Bell Laboratories , and after a 1997 split, at AT&T Labs Research. In 1997 I also visited the Computer Science Division at UC Berkeley. From 2012 to 2014 I was a principal researcher at Microsoft Research (Silicon Valley).
My research interests include Algorithms design, Data Mining, Machine Learning, Optimization, Networks, and more. I prefer a principled approach to modeling and design and I am always looking to learn and expand my horizons. In the span of my research career, I developed models and scalable algorithms in a wide range of areas including query processing and optimization, data summarization, content search and delivery, caching, prefetching, routing, streaming and distributed computation, fundamental graph algorithms and scalable mining of massive graphs. My work enables the leveraging of much larger data sets than previously possible. More details on my work can be found on my personal web page.
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One of the most basic problems for studying the "price of privacy over time" is the so called private counter problem, introduced by Dwork et al. (2010) and Chan et al. (2011). In this problem, we aim to track the number of events that occur over time, while hiding the existence of every single event. More specifically, in every time step $t\in[T]$ we learn (in an online fashion) that $\Delta_t\geq 0$ new events have occurred, and must respond with an estimate $n_t\approx\sum_{j=1}^t \Delta_j$. The privacy requirement is that all of the outputs together, across all time steps, satisfy event level differential privacy.
The main question here is how our error needs to depend on the total number of time steps $T$ and the total number of events $n$. Dwork et al. (2015) showed an upper bound of $O\left(\log(T)+\log^2(n)\right)$, and Henzinger et al. (2023) showed a lower bound of $\Omega\left(\min\{\log n, \log T\}\right)$. We show a new lower bound of $\Omega\left(\min\{n,\log T\}\right)$, which is tight w.r.t. the dependence on $T$, and is tight in the sparse case where $\log^2 n=O(\log T)$. Our lower bound has the following implications:
* We show that our lower bound extends to the online thresholds problem, where the goal is to privately answer many "quantile queries" when these queries are presented one-by-one. This resolves an open question of Bun et al. (2017).
* Our lower bound implies, for the first time, a separation between the number of mistakes obtainable by a private online learner and a non-private online learner. This partially resolves a COLT'22 open question published by Sanyal and Ramponi.
* Our lower bound also yields the first separation between the standard model of private online learning and a recently proposed relaxed variant of it, called private online prediction.
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The problem of learning threshold functions is a fundamental one in machine learning. Classical learning theory implies sample complexity of $O(\xi^{-1} \log(1/\beta))$ (for generalization error $\xi$ with confidence $1-\beta$). The private version of the problem, however, is more challenging and in particular, the sample complexity must depend on the size $|X|$ of the domain. Progress on quantifying this dependence, via lower and upper bounds, was made in a line of works over the past decade. In this paper, we finally close the gap for approximate-DP and provide a nearly tight upper bound of $\widetilde{O}(\log^* |X|)$, which matches a lower bound by Alon et al (that applies even with improper learning) and improves over a prior upper bound of $\widetilde{O}((\log^* |X|)^{1.5})$ by Kaplan et al. We also provide matching upper and lower bounds of $\tilde{\Theta}(2^{\log^*|X|})$ for the additive error of private quasi-concave optimization (a related and more general problem). Our improvement is achieved via the novel Reorder-Slice-Compute paradigm for private data analysis which we believe will have further applications.
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Composition theorems are general and powerful tools that facilitate privacy accounting across multiple data accesses from per-access privacy bounds. However they often result in weaker bounds compared with end-to-end analysis. Two popular tools that mitigate that are the exponential mechanism (or report noisy max) and the sparse vector technique. They were generalized in a couple of recent private selection/test frameworks, including the work by Liu and Talwar (STOC 2019), and Papernot and Steinke (ICLR 2022).
In this work, we first present an alternative framework for private selection and testing with a simpler privacy proof and equally-good utility guarantee. Second, we observe that the private selection framework (both previous ones and ours) can be applied to improve the accuracy/confidence trade-off for many fundamental privacy-preserving data-analysis tasks, including query releasing, top-k selection, and stable selection.
Finally, for online settings, we apply the private testing to design a mechanism for adaptive query releasing, which improves the sample complexity dependence on the confidence parameter for the celebrated private multiplicative weights algorithm of Hardt and Rothblum (FOCS 2010).
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CountSketch and Feature Hashing (the "hashing trick") are popular randomized dimensionality reduction methods that support recovery of $\ell_2$-heavy hitters (keys $i$ where $v_i^2 > \epsilon \|\boldsymbol{v}\|_2^2$) and approximate inner products. When the inputs are {\em not adaptive} (do not depend on prior outputs), classic estimators applied to a sketch of size $O(\ell/\epsilon)$ are accurate for a number of queries that is exponential in $\ell$. When inputs are adaptive, however, an adversarial input can be constructed after $O(\ell)$ queries with the classic estimator and the best known robust estimator only supports $\tilde{O}(\ell^2)$ queries. In this work we show that this quadratic dependence is in a sense inherent: We design an attack that after $O(\ell^2)$ queries produces an adversarial input vector whose sketch is highly biased. Our attack uses "natural" non-adaptive inputs (only the final adversarial input is chosen adaptively) and universally applies with any correct estimator, including one that is unknown to the attacker. In that, we expose inherent vulnerability of this fundamental method.
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Classical streaming algorithms operate under the (not always reasonable) assumption that the input stream is fixed in advance. Recently, there is a growing interest in designing robust streaming algorithms that provide provable guarantees even when the input stream is chosen adaptively as the execution progresses. We propose a new framework for robust streaming that combines techniques from two recently suggested frameworks by Hassidim et al. [NeurIPS 2020] and by Woodruff and Zhou [FOCS 2021]. These recently suggested frameworks rely on very different ideas, each with its own strengths and weaknesses. We combine these two frameworks into a single hybrid framework that obtains the "best of both worlds", thereby solving a question left open by Woodruff and Zhou.
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\texttt{CountSketch} is a popular dimensionality reduction technique that maps vectors to a lower-dimension using
a randomized set of linear measurements. The sketch has the property that the $\ell_2$-heavy hitters of a vector (entries with $v_i^2 \geq \frac{1}{k}\|\boldsymbol{v}\|^2_2$) can be recovered from its sketch. We study the robustness of the sketch in adaptive settings, such as online optimization, where input vectors may depend on the output from prior inputs. We show that the classic estimator can be attacked with a number of queries of the order of the sketch size and propose a robust estimator (for a slightly modified sketch) that allows for quadratic number of queries. We improve robustness by a factor of $\sqrt{k}$ (for $k$ heavy hitters) over prior approaches.
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Differentially private algorithms for common metric aggregation tasks, such as clustering or averaging, often have limited practicality due to their complexity or to the large number of data points that is required for accurate results.
We propose a simple and practical tool $\mathsf{FriendlyCore}$ that takes a set of points $\cD$ from an unrestricted (pseudo) metric space as input. When $\cD$ has effective diameter $r$, $\mathsf{FriendlyCore}$ returns a ``stable'' subset $\cC \subseteq \cD$ that includes all points, except possibly few outliers, and is {\em guaranteed} to have diameter $r$. $\mathsf{FriendlyCore}$ can be used to preprocess the input before privately aggregating it, potentially simplifying the aggregation or boosting its accuracy. Surprisingly, $\mathsf{FriendlyCore}$ is light-weight with no dependence on the dimension. We empirically demonstrate its advantages in boosting the accuracy of mean estimation and clustering tasks such as $k$-means and $k$-GMM, outperforming tailored methods.
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Clustering is a fundamental problem in data analysis. In differentially private clustering, the goal is to identify k cluster centers without disclosing information on individual data points. Despite significant research progress, the problem had so far resisted practical solutions. In this work we aim at providing simple implementable differentially private clustering algorithms that provide utility when the data is "easy", e.g., when there exists a significant separation between the clusters.
We propose a framework that allows us to apply non-private clustering algorithms to the easy instances and privately combine the results.
We are able to get improved sample complexity bounds in some cases of Gaussian mixtures and k-means. We complement our theoretical analysis with an empirical evaluation on synthetic data.
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Common datasets have the form of elements with keys (e.g., transactions and products) and the goal is to perform analytics on the aggregated form of key and frequency pairs. A weighted sample of keys by (a function of) frequency is a highly versatile summary that provides a sparse set of representative keys and supports approximate evaluations of query statistics. We propose private weighted sampling (PWS): A method that sanitizes a weighted sample as to ensure element-level differential privacy, while retaining its utility to the maximum extent possible. PWS maximizes the reporting probabilities of keys and estimation quality of a broad family of statistics. PWS improves over the state of the art even for the well-studied special case of private histograms, when no sampling is performed. We empirically observe significant performance gains of 20%-300% increase in key reporting for common Zipfian frequency distributions and accurate estimation with X2-8 lower frequencies. PWS is applied as a post-processing of a non-private sample, without requiring the original data. Therefore, it can be a seamless addition to existing implementations, such as those optimizes for distributed or streamed data. We believe that due to practicality and performance, PWS may become a method of choice in applications where privacy is desired.
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Optimization of a machine learning model is typically carried out by performing stochastic gradient updates on epochs that consist of randomly ordered training examples. This practice means that eachfraction of an epoch comprises an independent random sample of the training data that may not preserve informative structure present in the full data. We hypothesize that the training can be more effective, allowing each epoch to provide some of the benefits of multiple ones, with more principled, ``self-similar'' arrangements.
Our case study is matrix factorization, commonly used to learn metric embeddings of entities such as videos or words from example associations. We construct arrangements that preserve the weighted Jaccard similarities of rows and columns and experimentally observe that our arrangements yield training acceleration of 3\%-30\% on synthetic and recommendation datasets. Principled arrangements of training examples emerge as a novel and potentially powerful performance knob for SGD that merits further exploration.
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