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Experiment design has a rich history dating back over a century and has found many critical applications across various fields since then. The use and collection of users' data in experiments often involve sensitive personal information, so additional measures to protect individual privacy are required during data collection, storage, and usage. In this work, we focus on the rigorous protection of users' privacy (under the notion of differential privacy (DP)) while minimizing the trust toward service providers. Specifically, we consider the estimation of the average treatment effect (ATE) under DP, while only allowing the analyst to collect population-level statistics via secure aggregation, a distributed protocol enabling a service provider to aggregate information without accessing individual data. Although a vital component in modern A/B testing workflows, private distributed experimentation has not previously been studied. To achieve DP, we design local privatization mechanisms that are compatible with secure aggregation and analyze the utility, in terms of the width of confidence intervals, both asymptotically and non-asymptotically. We show how these mechanisms can be scaled up to handle the very large number of participants commonly found in practice. In addition, when introducing DP noise, it is imperative to cleverly split privacy budgets to estimate both the mean and variance of the outcomes and carefully calibrate the confidence intervals according to the DP noise. Last, we present comprehensive experimental evaluations of our proposed schemes and show the privacy-utility trade-offs in experiment design.

Preserving individual privacy while enabling collaborative data sharing is crucial for organizations. Synthetic data generation is one solution, producing artificial data that mirrors the statistical properties of private data. While numerous techniques have been devised under differential privacy, they predominantly assume data is centralized. However, data is often distributed across multiple clients in a federated manner. In this work, we initiate the study of federated synthetic tabular data generation. Building upon a SOTA central method known as AIM, we present DistAIM and FLAIM. We first show that it is straightforward to distribute AIM, extending a recent approach based on secure multi-party computation which necessitates additional overhead, making it less suited to federated scenarios. We then demonstrate that naively federating AIM can lead to substantial degradation in utility under the presence of heterogeneity. To mitigate both issues, we propose an augmented FLAIM approach that maintains a private proxy of heterogeneity. We simulate our methods across a range of benchmark datasets under different degrees of heterogeneity and show we can improve utility while reducing overhead., Comment: 19 pages

Answering database queries while preserving privacy is an important problem that has attracted considerable research attention in recent years. A canonical approach to this problem is to use synthetic data. That is, we replace the input database R with a synthetic database R* that preserves the characteristics of R, and use R* to answer queries. Existing solutions for relational data synthesis, however, either fail to provide strong privacy protection, or assume that R contains a single relation. In addition, it is challenging to extend the existing single-relation solutions to the case of multiple relations, because they are unable to model the complex correlations induced by the foreign keys. Therefore, multi-relational data synthesis with strong privacy guarantees is an open problem. In this paper, we address the above open problem by proposing PrivLava, the first solution for synthesizing relational data with foreign keys under differential privacy, a rigorous privacy framework widely adopted in both academia and industry. The key idea of PrivLava is to model the data distribution in R using graphical models, with latent variables included to capture the inter-relational correlations caused by foreign keys. We show that PrivLava supports arbitrary foreign key references that form a directed acyclic graph, and is able to tackle the common case when R contains a mixture of public and private relations. Extensive experiments on census data sets and the TPC-H benchmark demonstrate that PrivLava significantly outperforms its competitors in terms of the accuracy of aggregate queries processed on the synthetic data., Comment: This is an extended version of a SIGMOD 2023 paper

Data sketching is a critical tool for distinct counting, enabling multisets to be represented by compact summaries that admit fast cardinality estimates. Because sketches may be merged to summarize multiset unions, they are a basic building block in data warehouses. Although many practical sketches for cardinality estimation exist, none provide privacy when merging. We propose the first practical cardinality sketches that are simultaneously mergeable, differentially private (DP), and have low empirical errors. These introduce a novel randomized algorithm for performing logical operations on noisy bits, a tight privacy analysis, and provably optimal estimation. Our sketches dramatically outperform existing theoretical solutions in simulations and on real-world data., Comment: 28 pages, 5 figures

Neural network pruning is frequently used to compress over-parameterized networks by large amounts, while incurring only marginal drops in generalization performance. However, the impact of pruning on networks that have been highly optimized for efficient inference has not received the same level of attention. In this paper, we analyze the effect of pruning for computer vision, and study state-of-the-art ConvNets, such as the FBNetV3 family of models. We show that model pruning approaches can be used to further optimize networks trained through NAS (Neural Architecture Search). The resulting family of pruned models can consistently obtain better performance than existing FBNetV3 models at the same level of computation, and thus provide state-of-the-art results when trading off between computational complexity and generalization performance on the ImageNet benchmark. In addition to better generalization performance, we also demonstrate that when limited computation resources are available, pruning FBNetV3 models incur only a fraction of GPU-hours involved in running a full-scale NAS.

Streaming interactive proofs (SIPs) enable a space-bounded algorithm with one-pass access to a massive stream of data to verify a computation that requires large space, by communicating with a powerful but untrusted prover. This work initiates the study of zero-knowledge proofs for data streams. We define the notion of zero-knowledge in the streaming setting and construct zero-knowledge SIPs for the two main algorithmic building blocks in the streaming interactive proofs literature: the sumcheck and polynomial evaluation protocols. To the best of our knowledge all known streaming interactive proofs are based on either of these tools, and indeed, this allows us to obtain zero-knowledge SIPs for central streaming problems such as index, point and range queries, median, frequency moments, and inner product. Our protocols are efficient in terms of time and space, as well as communication: the verifier algorithm's space complexity is $\mathrm{polylog}(n)$ and, after a non-interactive setup that uses a random string of near-linear length, the remaining parameters are $n^{o(1)}$. En route, we develop an algorithmic toolkit for designing zero-knowledge data stream protocols, consisting of an algebraic streaming commitment protocol and a temporal commitment protocol.Our analyses rely on delicate algebraic and information-theoretic arguments and reductions from average-case communication complexity.

We consider the federated frequency estimation problem, where each user holds a private item $X_i$ from a size-$d$ domain and a server aims to estimate the empirical frequency (i.e., histogram) of $n$ items with $n \ll d$. Without any security and privacy considerations, each user can communicate its item to the server by using $\log d$ bits. A naive application of secure aggregation protocols would, however, require $d\log n$ bits per user. Can we reduce the communication needed for secure aggregation, and does security come with a fundamental cost in communication? In this paper, we develop an information-theoretic model for secure aggregation that allows us to characterize the fundamental cost of security and privacy in terms of communication. We show that with security (and without privacy) $\Omega\left( n \log d \right)$ bits per user are necessary and sufficient to allow the server to compute the frequency distribution. This is significantly smaller than the $d\log n$ bits per user needed by the naive scheme, but significantly higher than the $\log d$ bits per user needed without security. To achieve differential privacy, we construct a linear scheme based on a noisy sketch which locally perturbs the data and does not require a trusted server (a.k.a. distributed differential privacy). We analyze this scheme under $\ell_2$ and $\ell_\infty$ loss. By using our information-theoretic framework, we show that the scheme achieves the optimal accuracy-privacy trade-off with optimal communication cost, while matching the performance in the centralized case where data is stored in the central server.

We address two major obstacles to practical use of supervised classifiers on distributed private data. Whether a classifier was trained by a federation of cooperating clients or trained centrally out of distribution, (1) the output scores must be calibrated, and (2) performance metrics must be evaluated -- all without assembling labels in one place. In particular, we show how to perform calibration and compute precision, recall, accuracy and ROC-AUC in the federated setting under three privacy models (i) secure aggregation, (ii) distributed differential privacy, (iii) local differential privacy. Our theorems and experiments clarify tradeoffs between privacy, accuracy, and data efficiency. They also help decide whether a given application has sufficient data to support federated calibration and evaluation., Comment: 24 pages

There is great demand for scalable, secure, and efficient privacy-preserving machine learning models that can be trained over distributed data. While deep learning models typically achieve the best results in a centralized non-secure setting, different models can excel when privacy and communication constraints are imposed. Instead, tree-based approaches such as XGBoost have attracted much attention for their high performance and ease of use; in particular, they often achieve state-of-the-art results on tabular data. Consequently, several recent works have focused on translating Gradient Boosted Decision Tree (GBDT) models like XGBoost into federated settings, via cryptographic mechanisms such as Homomorphic Encryption (HE) and Secure Multi-Party Computation (MPC). However, these do not always provide formal privacy guarantees, or consider the full range of hyperparameters and implementation settings. In this work, we implement the GBDT model under Differential Privacy (DP). We propose a general framework that captures and extends existing approaches for differentially private decision trees. Our framework of methods is tailored to the federated setting, and we show that with a careful choice of techniques it is possible to achieve very high utility while maintaining strong levels of privacy., Comment: Full version of a paper to appear at ACM CCS'22

Differential Privacy (DP) is often presented as a strong privacy-enhancing technology with broad applicability and advocated as a de-facto standard for releasing aggregate statistics on sensitive data. However, in many embodiments, DP introduces a new attack surface: a malicious entity entrusted with releasing statistics could manipulate the results and use the randomness of DP as a convenient smokescreen to mask its nefariousness. Since revealing the random noise would obviate the purpose of introducing it, the miscreant may have a perfect alibi. To close this loophole, we introduce the idea of \textit{Verifiable Differential Privacy}, which requires the publishing entity to output a zero-knowledge proof that convinces an efficient verifier that the output is both DP and reliable. Such a definition might seem unachievable, as a verifier must validate that DP randomness was generated faithfully without learning anything about the randomness itself. We resolve this paradox by carefully mixing private and public randomness to compute verifiable DP counting queries with theoretical guarantees and show that it is also practical for real-world deployment. We also demonstrate that computational assumptions are necessary by showing a separation between information-theoretic DP and computational DP under our definition of verifiability.

Cross-device Federated Learning is an increasingly popular machine learning setting to train a model by leveraging a large population of client devices with high privacy and security guarantees. However, communication efficiency remains a major bottleneck when scaling federated learning to production environments, particularly due to bandwidth constraints during uplink communication. In this paper, we formalize and address the problem of compressing client-to-server model updates under the Secure Aggregation primitive, a core component of Federated Learning pipelines that allows the server to aggregate the client updates without accessing them individually. In particular, we adapt standard scalar quantization and pruning methods to Secure Aggregation and propose Secure Indexing, a variant of Secure Aggregation that supports quantization for extreme compression. We establish state-of-the-art results on LEAF benchmarks in a secure Federated Learning setup with up to 40$\times$ compression in uplink communication with no meaningful loss in utility compared to uncompressed baselines.

With the recent bloom of data, there is a huge surge in threats against individuals' private information. Various techniques for optimizing privacy-preserving data analysis are at the focus of research in the recent years. In this paper, we analyse the impact of sampling on the utility of the standard techniques of frequency estimation, which is at the core of large-scale data analysis, of the locally deferentially private data-release under a pure protocol. We study the case in a distributed environment of data sharing where the values are reported by various nodes to the central server, e.g., cross-device Federated Learning. We show that if we introduce some random sampling of the nodes in order to reduce the cost of communication, the standard existing estimators fail to remain unbiased. We propose a new unbiased estimator in the context of sampling each node with certain probability and compute various statistical summaries of the data using it. We propose a way of sampling each node with personalized sampling probabilities as a step to further generalisation, which leads to some interesting open questions in the end. We analyse the accuracy of our proposed estimators on synthetic datasets to gather some insight on the trade-off between communication cost, privacy, and utility.

Given a trained model and a data sample, membership-inference (MI) attacks predict whether the sample was in the model's training set. A common countermeasure against MI attacks is to utilize differential privacy (DP) during model training to mask the presence of individual examples. While this use of DP is a principled approach to limit the efficacy of MI attacks, there is a gap between the bounds provided by DP and the empirical performance of MI attacks. In this paper, we derive bounds for the \textit{advantage} of an adversary mounting a MI attack, and demonstrate tightness for the widely-used Gaussian mechanism. We further show bounds on the \textit{confidence} of MI attacks. Our bounds are much stronger than those obtained by DP analysis. For example, analyzing a setting of DP-SGD with $\epsilon=4$ would obtain an upper bound on the advantage of $\approx0.36$ based on our analyses, while getting bound of $\approx 0.97$ using the analysis of previous work that convert $\epsilon$ to membership inference bounds. Finally, using our analysis, we provide MI metrics for models trained on CIFAR10 dataset. To the best of our knowledge, our analysis provides the state-of-the-art membership inference bounds for the privacy.

Advances in communications, storage and computational technology allow significant quantities of data to be collected and processed by distributed devices. Combining the information from these endpoints can realize significant societal benefit but presents challenges in protecting the privacy of individuals, especially important in an increasingly regulated world. Differential privacy (DP) is a technique that provides a rigorous and provable privacy guarantee for aggregation and release. The Shuffle Model for DP has been introduced to overcome challenges regarding the accuracy of local-DP algorithms and the privacy risks of central-DP. In this work we introduce a new protocol for vector aggregation in the context of the Shuffle Model. The aim of this paper is twofold; first, we provide a single message protocol for the summation of real vectors in the Shuffle Model, using advanced composition results. Secondly, we provide an improvement on the bound on the error achieved through using this protocol through the implementation of a Discrete Fourier Transform, thereby minimizing the initial error at the expense of the loss in accuracy through the transformation itself. This work will further the exploration of more sophisticated structures such as matrices and higher-dimensional tensors in this context, both of which are reliant on the functionality of the vector case., Comment: 16 pages, 5 figures, in: IEEE Transactions on Information Forensics and Security (TIFS), 2022. arXiv admin note: substantial text overlap with arXiv:2112.05464

Joining records with all other records that meet a linkage condition can result in an astronomically large number of combinations due to many-to-many relationships. For such challenging (acyclic) joins, a random sample over the join result is a practical alternative to working with the oversized join result. Whereas prior works are limited to uniform join sampling where each join row is assigned the same probability, the scope is extended in this work to weighted sampling to support emerging applications such as scientific discovery in observational data and privacy-preserving query answering. Notwithstanding some naive methods, this work presents the first approach for weighted random sampling from join results. Due to a lack of baselines, experiments over various join types and real-world data sets are conducted to show substantial memory savings and competitive performance with main-memory index-based approaches in the equal-probability setting. In contrast to existing uniform sampling approaches that require prepared structures that occupy contested resources to squeeze out slightly faster query-times, the proposed approaches exhibit qualities that are urgently needed in practice, namely reduced memory footprint, streaming operation, support for selections, outer joins, semi joins and anti joins and unequal-probability sampling. All pertinent code and data can be found at: https://github.com/shekelyan/weightedjoinsampling, Comment: 14 pages, 12 figures, 6 tables

In this work we introduce a new protocol for vector aggregation in the context of the Shuffle Model, a recent model within Differential Privacy (DP). It sits between the Centralized Model, which prioritizes the level of accuracy over the secrecy of the data, and the Local Model, for which an improvement in trust is counteracted by a much higher noise requirement. The Shuffle Model was developed to provide a good balance between these two models through the addition of a shuffling step, which unbinds the users from their data whilst maintaining a moderate noise requirement. We provide a single message protocol for the summation of real vectors in the Shuffle Model, using advanced composition results. Our contribution provides a mechanism to enable private aggregation and analysis across more sophisticated structures such as matrices and higher-dimensional tensors, both of which are reliant on the functionality of the vector case., Comment: 17 pages, 3 figures, in: British International Conference on Databases (BICOD21), London, UK, 28 Mar 2022

Federated analytics seeks to compute accurate statistics from data distributed across users' devices while providing a suitable privacy guarantee and being practically feasible to implement and scale. In this paper, we show how a strong $(\epsilon, \delta)$-Differential Privacy (DP) guarantee can be achieved for the fundamental problem of histogram generation in a federated setting, via a highly practical sampling-based procedure that does not add noise to disclosed data. Given the ubiquity of sampling in practice, we thus obtain a DP guarantee almost for free, avoid over-estimating histogram counts, and allow easy reasoning about how privacy guarantees may obscure minorities and outliers. Using such histograms, related problems such as heavy hitters and quantiles can be answered with provable error and privacy guarantees. Experimental results show that our sample-and-threshold approach is accurate and scalable., Comment: 15 pages In AISTATS 2022

The vulnerability of machine learning models to membership inference attacks has received much attention in recent years. However, existing attacks mostly remain impractical due to having high false positive rates, where non-member samples are often erroneously predicted as members. This type of error makes the predicted membership signal unreliable, especially since most samples are non-members in real world applications. In this work, we argue that membership inference attacks can benefit drastically from \emph{difficulty calibration}, where an attack's predicted membership score is adjusted to the difficulty of correctly classifying the target sample. We show that difficulty calibration can significantly reduce the false positive rate of a variety of existing attacks without a loss in accuracy., Comment: 16 pages

We introduce Opacus, a free, open-source PyTorch library for training deep learning models with differential privacy (hosted at opacus.ai). Opacus is designed for simplicity, flexibility, and speed. It provides a simple and user-friendly API, and enables machine learning practitioners to make a training pipeline private by adding as little as two lines to their code. It supports a wide variety of layers, including multi-head attention, convolution, LSTM, GRU (and generic RNN), and embedding, right out of the box and provides the means for supporting other user-defined layers. Opacus computes batched per-sample gradients, providing higher efficiency compared to the traditional "micro batch" approach. In this paper we present Opacus, detail the principles that drove its implementation and unique features, and benchmark it against other frameworks for training models with differential privacy as well as standard PyTorch., Comment: Privacy in Machine Learning (PriML) workshop, NeurIPS 2021

Sharing sensitive data is vital in enabling many modern data analysis and machine learning tasks. However, current methods for data release are insufficiently accurate or granular to provide meaningful utility, and they carry a high risk of deanonymization or membership inference attacks. In this paper, we propose a differentially private synthetic data generation solution with a focus on the compelling domain of location data. We present two methods with high practical utility for generating synthetic location data from real locations, both of which protect the existence and true location of each individual in the original dataset. Our first, partitioning-based approach introduces a novel method for privately generating point data using kernel density estimation, in addition to employing private adaptations of classic statistical techniques, such as clustering, for private partitioning. Our second, network-based approach incorporates public geographic information, such as the road network of a city, to constrain the bounds of synthetic data points and hence improve the accuracy of the synthetic data. Both methods satisfy the requirements of differential privacy, while also enabling accurate generation of synthetic data that aims to preserve the distribution of the real locations. We conduct experiments using three large-scale location datasets to show that the proposed solutions generate synthetic location data with high utility and strong similarity to the real datasets. We highlight some practical applications for our work by applying our synthetic data to a range of location analytics queries, and we demonstrate that our synthetic data produces near-identical answers to the same queries compared to when real data is used. Our results show that the proposed approaches are practical solutions for sharing and analyzing sensitive location data privately.

Sharing trajectories is beneficial for many real-world applications, such as managing disease spread through contact tracing and tailoring public services to a population's travel patterns. However, public concern over privacy and data protection has limited the extent to which this data is shared. Local differential privacy enables data sharing in which users share a perturbed version of their data, but existing mechanisms fail to incorporate user-independent public knowledge (e.g., business locations and opening times, public transport schedules, geo-located tweets). This limitation makes mechanisms too restrictive, gives unrealistic outputs, and ultimately leads to low practical utility. To address these concerns, we propose a local differentially private mechanism that is based on perturbing hierarchically-structured, overlapping $n$-grams (i.e., contiguous subsequences of length $n$) of trajectory data. Our mechanism uses a multi-dimensional hierarchy over publicly available external knowledge of real-world places of interest to improve the realism and utility of the perturbed, shared trajectories. Importantly, including real-world public data does not negatively affect privacy or efficiency. Our experiments, using real-world data and a range of queries, each with real-world application analogues, demonstrate the superiority of our approach over a range of alternative methods.

Private data generated by edge devices -- from smart phones to automotive electronics -- are highly informative when aggregated but can be damaging when mishandled. A variety of solutions are being explored but have not yet won the public's trust and full backing of mobile platforms. In this work, we propose numerical aggregation protocols that empirically improve upon prior art, while providing comparable local differential privacy guarantees. Sharing a single private bit per value supports privacy metering that enable privacy controls and guarantees that are not covered by differential privacy. We put emphasis on the ease of implementation, compatibility with existing methods, and compelling empirical performance., Comment: 15 pages

We study the fundamental problem of frequency estimation under both privacy and communication constraints, where the data is distributed among $k$ parties. We consider two application scenarios: (1) one-shot, where the data is static and the aggregator conducts a one-time computation; and (2) streaming, where each party receives a stream of items over time and the aggregator continuously monitors the frequencies. We adopt the model of multiparty differential privacy (MDP), which is more general than local differential privacy (LDP) and (centralized) differential privacy. Our protocols achieve optimality (up to logarithmic factors) permissible by the more stringent of the two constraints. In particular, when specialized to the $\varepsilon$-LDP model, our protocol achieves an error of $\sqrt{k}/(e^{\Theta(\varepsilon)}-1)$ using $O(k\max\{ \varepsilon, \frac{1}{\varepsilon} \})$ bits of communication and $O(k \log u)$ bits of public randomness, where $u$ is the size of the domain.

Private collection of statistics from a large distributed population is an important problem, and has led to large scale deployments from several leading technology companies. The dominant approach requires each user to randomly perturb their input, leading to guarantees in the local differential privacy model. In this paper, we place the various approaches that have been suggested into a common framework, and perform an extensive series of experiments to understand the tradeoffs between different implementation choices. Our conclusion is that for the core problems of frequency estimation and heavy hitter identification, careful choice of algorithms can lead to very effective solutions that scale to millions of users, Comment: 13 pages; Updated figures (7,8,10) and minor corrections

Estimating the distribution and quantiles of data is a foundational task in data mining and data science. We study algorithms which provide accurate results for extreme quantile queries using a small amount of space, thus helping to understand the tails of the input distribution. Namely, we focus on two recent state-of-the-art solutions: $t$-digest and ReqSketch. While $t$-digest is a popular compact summary which works well in a variety of settings, ReqSketch comes with formal accuracy guarantees at the cost of its size growing as new observations are inserted. In this work, we provide insight into which conditions make one preferable to the other. Namely, we show how to construct inputs for $t$-digest that induce an almost arbitrarily large error and demonstrate that it fails to provide accurate results even on i.i.d. samples from a highly non-uniform distribution. We propose practical improvements to ReqSketch, making it faster than $t$-digest, while its error stays bounded on any instance. Still, our results confirm that $t$-digest remains more accurate on the ``non-adversarial'' data encountered in practice., Comment: Updated experiments, improved presentation. To appear in KDD 2021

Given an $n \times d$ dimensional dataset $A$, a projection query specifies a subset $C \subseteq [d]$ of columns which yields a new $n \times |C|$ array. We study the space complexity of computing data analysis functions over such subspaces, including heavy hitters and norms, when the subspaces are revealed only after observing the data. We show that this important class of problems is typically hard: for many problems, we show $2^{\Omega(d)}$ lower bounds. However, we present upper bounds which demonstrate space dependency better than $2^d$. That is, for $c,c' \in (0,1)$ and a parameter $N=2^d$ an $N^c$-approximation can be obtained in space $\min(N^{c'},n)$, showing that it is possible to improve on the na\"{i}ve approach of keeping information for all $2^d$ subsets of $d$ columns. Our results are based on careful constructions of instances using coding theory and novel combinatorial reductions that exhibit such space-approximation tradeoffs.

Estimating ranks, quantiles, and distributions over streaming data is a central task in data analysis and monitoring. Given a stream of $n$ items from a data universe equipped with a total order, the task is to compute a sketch (data structure) of size polylogarithmic in $n$. Given the sketch and a query item $y$, one should be able to approximate its rank in the stream, i.e., the number of stream elements smaller than or equal to $y$. Most works to date focused on additive $\varepsilon n$ error approximation, culminating in the KLL sketch that achieved optimal asymptotic behavior. This paper investigates multiplicative $(1\pm\varepsilon)$-error approximations to the rank. Practical motivation for multiplicative error stems from demands to understand the tails of distributions, and hence for sketches to be more accurate near extreme values. The most space-efficient algorithms due to prior work store either $O(\log(\varepsilon^2 n)/\varepsilon^2)$ or $O(\log^3(\varepsilon n)/\varepsilon)$ universe items. We present a randomized sketch storing $O(\log^{1.5}(\varepsilon n)/\varepsilon)$ items that can $(1\pm\varepsilon)$-approximate the rank of each universe item with high constant probability; this space bound is within an $O(\sqrt{\log(\varepsilon n)})$ factor of optimal. Our algorithm does not require prior knowledge of the stream length and is fully mergeable, rendering it suitable for parallel and distributed computing environments., Comment: Final version of the paper to appear in Journal of the ACM. Compared to the previous version, we removed any restrictions on the accuracy parameters in the main result and thoroughly revised the paper. 48 pages, 2 figures

Federated learning (FL) is a machine learning setting where many clients (e.g. mobile devices or whole organizations) collaboratively train a model under the orchestration of a central server (e.g. service provider), while keeping the training data decentralized. FL embodies the principles of focused data collection and minimization, and can mitigate many of the systemic privacy risks and costs resulting from traditional, centralized machine learning and data science approaches. Motivated by the explosive growth in FL research, this paper discusses recent advances and presents an extensive collection of open problems and challenges., Comment: Published in Foundations and Trends in Machine Learning Vol 4 Issue 1. See: https://www.nowpublishers.com/article/Details/MAL-083

Parameterized complexity attempts to give a more fine-grained analysis of the complexity of problems: instead of measuring the running time as a function of only the input size, we analyze the running time with respect to additional parameters. This approach has proven to be highly successful in delineating our understanding of \NP-hard problems. Given this success with the TIME resource, it seems but natural to use this approach for dealing with the SPACE resource. First attempts in this direction have considered a few individual problems, with some success: Fafianie and Kratsch [MFCS'14] and Chitnis et al. [SODA'15] introduced the notions of streaming kernels and parameterized streaming algorithms respectively. For example, the latter shows how to refine the $\Omega(n^2)$ bit lower bound for finding a minimum Vertex Cover (VC) in the streaming setting by designing an algorithm for the parameterized $k$-VC problem which uses $O(k^{2}\log n)$ bits. In this paper, we initiate a systematic study of graph problems from the paradigm of parameterized streaming algorithms. We first define a natural hierarchy of space complexity classes of FPS, SubPS, SemiPS, SupPS and BrutePS, and then obtain tight classifications for several well-studied graph problems such as Longest Path, Feedback Vertex Set, Dominating Set, Girth, Treewidth, etc. into this hierarchy. (see paper for full abstract), Comment: Extended abstract in IPEC 2019. arXiv admin note: text overlap with arXiv:1603.05715 by other authors

Scalable algorithms to solve optimization and regression tasks even approximately, are needed to work with large datasets. In this paper we study efficient techniques from matrix sketching to solve a variety of convex constrained regression problems. We adopt "Iterative Hessian Sketching" (IHS) and show that the fast CountSketch and sparse Johnson-Lindenstrauss Transforms yield state-of-the-art accuracy guarantees under IHS, while drastically improving the time cost. As a result, we obtain significantly faster algorithms for constrained regression, for both sparse and dense inputs. Our empirical results show that we can summarize data roughly 100x faster for sparse data, and, surprisingly, 10x faster on dense data! Consequently, solutions accurate to within machine precision of the optimal solution can be found much faster than the previous state of the art.

Problems involving the efficient arrangement of simple objects, as captured by bin packing and makespan scheduling, are fundamental tasks in combinatorial optimization. These are well understood in the traditional online and offline cases, but have been less well-studied when the volume of the input is truly massive, and cannot even be read into memory. This is captured by the streaming model of computation, where the aim is to approximate the cost of the solution in one pass over the data, using small space. As a result, streaming algorithms produce concise input summaries that approximately preserve the optimum value. We design the first efficient streaming algorithms for these fundamental problems in combinatorial optimization. For Bin Packing, we provide a streaming asymptotic $1+\varepsilon$-approximation with $\widetilde{O}\left(\frac{1}{\varepsilon}\right)$ memory, where $\widetilde{O}$ hides logarithmic factors. Moreover, such a space bound is essentially optimal. Our algorithm implies a streaming $d+\varepsilon$-approximation for Vector Bin Packing in $d$ dimensions, running in space $\widetilde{O}\left(\frac{d}{\varepsilon}\right)$. For the related Vector Scheduling problem, we show how to construct an input summary in space $\widetilde{O}(d^2\cdot m / \varepsilon^2)$ that preserves the optimum value up to a factor of $2 - \frac{1}{m} +\varepsilon$, where $m$ is the number of identical machines., Comment: 19 pages, 1 figure, submitted

Quantiles, such as the median or percentiles, provide concise and useful information about the distribution of a collection of items, drawn from a totally ordered universe. We study data structures, called quantile summaries, which keep track of all quantiles, up to an error of at most $\varepsilon$. That is, an $\varepsilon$-approximate quantile summary first processes a stream of items and then, given any quantile query $0\le \phi\le 1$, returns an item from the stream, which is a $\phi'$-quantile for some $\phi' = \phi \pm \varepsilon$. We focus on comparison-based quantile summaries that can only compare two items and are otherwise completely oblivious of the universe. The best such deterministic quantile summary to date, due to Greenwald and Khanna (SIGMOD '01), stores at most $O(\frac{1}{\varepsilon}\cdot \log \varepsilon N)$ items, where $N$ is the number of items in the stream. We prove that this space bound is optimal by showing a matching lower bound. Our result thus rules out the possibility of constructing a deterministic comparison-based quantile summary in space $f(\varepsilon)\cdot o(\log N)$, for any function $f$ that does not depend on $N$. As a corollary, we improve the lower bound for biased quantiles, which provide a stronger, relative-error guarantee of $(1\pm \varepsilon)\cdot \phi$, and for other related computational tasks., Comment: 20 pages, 2 figures, major revison of the construction (Sec. 3) and some other parts of the paper

Counting the fraction of a population having an input within a specified interval i.e. a \emph{range query}, is a fundamental data analysis primitive. Range queries can also be used to compute other interesting statistics such as \emph{quantiles}, and to build prediction models. However, frequently the data is subject to privacy concerns when it is drawn from individuals, and relates for example to their financial, health, religious or political status. In this paper, we introduce and analyze methods to support range queries under the local variant of differential privacy, an emerging standard for privacy-preserving data analysis. The local model requires that each user releases a noisy view of her private data under a privacy guarantee. While many works address the problem of range queries in the trusted aggregator setting, this problem has not been addressed specifically under untrusted aggregation (local DP) model even though many primitives have been developed recently for estimating a discrete distribution. We describe and analyze two classes of approaches for range queries, based on hierarchical histograms and the Haar wavelet transform. We show that both have strong theoretical accuracy guarantees on variance. In practice, both methods are fast and require minimal computation and communication resources. Our experiments show that the wavelet approach is most accurate in high privacy settings, while the hierarchical approach dominates for weaker privacy requirements.

Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as $k$-center, $k$-median, and $k$-means. Such algorithms need to be both time and and space efficient. In this paper, we address the problem of correlation clustering in the dynamic data stream model. The stream consists of updates to the edge weights of a graph on $n$ nodes and the goal is to find a node-partition such that the end-points of negative-weight edges are typically in different clusters whereas the end-points of positive-weight edges are typically in the same cluster. We present polynomial-time, $O(n\cdot \ \mbox{polylog}~n)$-space approximation algorithms for natural problems that arise. We first develop data structures based on linear sketches that allow the "quality" of a given node-partition to be measured. We then combine these data structures with convex programming and sampling techniques to solve the relevant approximation problem. Unfortunately, the standard LP and SDP formulations are not obviously solvable in $O(n\cdot \mbox{polylog}~n)$-space. Our work presents space-efficient algorithms for the convex programming required, as well as approaches to reduce the adaptivity of the sampling.

We consider the classic maximal and maximum independent set problems in three models of graph streams: In the edge-arrival model we see a stream of edges which collectively define a graph, this model has been well-studied for a variety of problems. We first show that the space complexity for a one-pass streaming algorithm to find a maximal independent set is quadratic (i.e. we must store all edges). We further show that the problem does not become much easier if we only require approximate maximality. In the "explicit" vertex stream model, the input stream is a sequence of vertices making up the graph, where every vertex arrives along with its incident edges that connect to previously arrived vertices. Various graph problems require substantially less space to solve in this setting than for edge-arrival streams. We show that every one-pass $c$-approximation algorithm for maximum independent set (MIS) on explicit vertex streams requires space $\Omega(\frac{n^2}{c^7})$, where $n$ is the number of vertices of the input graph, and it is already known that space $\tilde{\Theta}(\frac{n^2}{c^2})$ is necessary and sufficient in the edge arrival model (Halld\'orsson et al. 2012). The MIS problem is thus not significantly easier to solve under the explicit vertex arrival order assumption. Our result is proved via a reduction to a new multi-party communication problem closely related to pointer jumping. In the "implicit" vertex stream model, the input stream consists of a sequence of objects, one per vertex. The algorithm is equipped with a function that can map a pair of objects to the presence or absence of an edge, thus defining the graph. This model captures, for example, geometric intersection graphs such as unit disc graphs. Our final set of results consists of several improved upper and lower bounds for ball intersection graphs, in both explicit and implicit streams.

Work on approximate linear algebra has led to efficient distributed and streaming algorithms for problems such as approximate matrix multiplication, low rank approximation, and regression, primarily for the Euclidean norm $\ell_2$. We study other $\ell_p$ norms, which are more robust for $p < 2$, and can be used to find outliers for $p > 2$. Unlike previous algorithms for such norms, we give algorithms that are (1) deterministic, (2) work simultaneously for every $p \geq 1$, including $p = \infty$, and (3) can be implemented in both distributed and streaming environments. We apply our results to $\ell_p$-regression, entrywise $\ell_1$-low rank approximation, and approximate matrix multiplication.

Many analysis and machine learning tasks require the availability of marginal statistics on multidimensional datasets while providing strong privacy guarantees for the data subjects. Applications for these statistics range from finding correlations in the data to fitting sophisticated prediction models. In this paper, we provide a set of algorithms for materializing marginal statistics under the strong model of local differential privacy. We prove the first tight theoretical bounds on the accuracy of marginals compiled under each approach, perform empirical evaluation to confirm these bounds, and evaluate them for tasks such as modeling and correlation testing. Our results show that releasing information based on (local) Fourier transformations of the input is preferable to alternatives based directly on (local) marginals.

A current challenge for data management systems is to support the construction and maintenance of machine learning models over data that is large, multi-dimensional, and evolving. While systems that could support these tasks are emerging, the need to scale to distributed, streaming data requires new models and algorithms. In this setting, as well as computational scalability and model accuracy, we also need to minimize the amount of communication between distributed processors, which is the chief component of latency. We study Bayesian networks, the workhorse of graphical models, and present a communication-efficient method for continuously learning and maintaining a Bayesian network model over data that is arriving as a distributed stream partitioned across multiple processors. We show a strategy for maintaining model parameters that leads to an exponential reduction in communication when compared with baseline approaches to maintain the exact MLE (maximum likelihood estimation). Meanwhile, our strategy provides similar prediction errors for the target distribution and for classification tasks.

Many data sources can be interpreted as time-series, and a key problem is to identify which pairs out of a large collection of signals are highly correlated. We expect that there will be few, large, interesting correlations, while most signal pairs do not have any strong correlation. We abstract this as the problem of identifying the highly correlated pairs in a collection of n mostly pairwise uncorrelated random variables, where observations of the variables arrives as a stream. Dimensionality reduction can remove dependence on the number of observations, but further techniques are required to tame the quadratic (in n) cost of a search through all possible pairs. We develop a new algorithm for rapidly finding large correlations based on sketch techniques with an added twist: we quickly generate sketches of random combinations of signals, and use these in concert with ideas from coding theory to decode the identity of correlated pairs. We prove correctness and compare performance and effectiveness with the best LSH (locality sensitive hashing) based approach., Comment: 15 pages

Concern about how to aggregate sensitive user data without compromising individual privacy is a major barrier to greater availability of data. The model of differential privacy has emerged as an accepted model to release sensitive information while giving a statistical guarantee for privacy. Many different algorithms are possible to address different target functions. We focus on the core problem of count queries, and seek to design mechanisms to release data associated with a group of n individuals. Prior work has focused on designing mechanisms by raw optimization of a loss function, without regard to the consequences on the results. This can leads to mechanisms with undesirable properties, such as never reporting some outputs (gaps), and overreporting others (spikes). We tame these pathological behaviors by introducing a set of desirable properties that mechanisms can obey. Any combination of these can be satisfied by solving a linear program (LP) which minimizes a cost function, with constraints enforcing the properties. We focus on a particular cost function, and provide explicit constructions that are optimal for certain combinations of properties, and show a closed form for their cost. In the end, there are only a handful of distinct optimal mechanisms to choose between: one is the well-known (truncated) geometric mechanism; the second a novel mechanism that we introduce here, and the remainder are found as the solution to particular LPs. These all avoid the bad behaviors we identify. We demonstrate in a set of experiments on real and synthetic data which is preferable in practice, for different combinations of data distributions, constraints, and privacy parameters.

We study the problem of estimating the size of independent sets in a graph $G$ defined by a stream of edges. Our approach relies on the Caro-Wei bound, which expresses the desired quantity in terms of a sum over nodes of the reciprocal of their degrees, denoted by $\beta(G)$. Our results show that $\beta(G)$ can be approximated accurately, based on a provided lower bound on $\beta$. Stronger results are possible when the edges are promised to arrive grouped by an incident node. In this setting, we obtain a value that is at most a logarithmic factor below the true value of $\beta$ and no more than the true independent set size. To justify the form of this bound, we also show an $\Omega(n/\beta)$ lower bound on any algorithm that approximates $\beta$ up to a constant factor.

Estimating the size of the maximum matching is a canonical problem in graph algorithms, and one that has attracted extensive study over a range of different computational models. We present improved streaming algorithms for approximating the size of maximum matching with sparse (bounded arboricity) graphs. * Insert-Only Streams: We present a one-pass algorithm that takes O(c log^2 n) space and approximates the size of the maximum matching in graphs with arboricity c within a factor of O(c). This improves significantly on the state-of-the-art O~(cn^{2/3})-space streaming algorithms. * Dynamic Streams: Given a dynamic graph stream (i.e., inserts and deletes) of edges of an underlying c-bounded arboricity graph, we present a one-pass algorithm that uses space O~(c^{10/3}n^{2/3}) and returns an O(c)-estimator for the size of the maximum matching. This algorithm improves the state-of-the-art O~(cn^{4/5})-space algorithms, where the O~(.) notation hides logarithmic in $n$ dependencies. In contrast to the previous works, our results take more advantage of the streaming access to the input and characterize the matching size based on the ordering of the edges in the stream in addition to the degree distributions and structural properties of the sparse graphs., Comment: 12 pages

In this paper we present a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams (where the input graph is defined by a sequence of edge/hyperedge insertions and deletions) and distributed systems such as MapReduce. In the case of dynamic graph streams, we use this primitive to prove the following results: -- Matching: First, there exists an $\tilde{O}(k^2)$ space algorithm that returns an exact maximum matching on the assumption the cardinality is at most $k$. The best previous algorithm used $\tilde{O}(kn)$ space where $n$ is the number of vertices in the graph and we prove our result is optimal up to logarithmic factors. Our algorithm has $\tilde{O}(1)$ update time. Second, there exists an $\tilde{O}(n^2/\alpha^3)$ space algorithm that returns an $\alpha$-approximation for matchings of arbitrary size. (Assadi et al. (2015) showed that this was optimal and independently and concurrently established the same upper bound.) We generalize both results for weighted matching. Third, there exists an $\tilde{O}(n^{4/5})$ space algorithm that returns a constant approximation in graphs with bounded arboricity. -- Vertex Cover and Hitting Set: There exists an $\tilde{O}(k^d)$ space algorithm that solves the minimum hitting set problem where $d$ is the cardinality of the input sets and $k$ is an upper bound on the size of the minimum hitting set. We prove this is optimal up to logarithmic factors. Our algorithm has $\tilde{O}(1)$ update time. The case $d=2$ corresponds to minimum vertex cover. Finally, we consider a larger family of parameterized problems (including $b$-matching, disjoint paths, vertex coloring among others) for which our subgraph sampling primitive yields fast, small-space dynamic graph stream algorithms. We then show lower bounds for natural problems outside this family.