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  1. 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 ε n error approximation, culminating in the KLL sketch that achieved optimal asymptotic behavior. This paper investigates multiplicative (1 ± ε)-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 (ε 2 n )/ε 2 ) or O (log  3 (ε n )/ε) universe items. We present a randomized sketch storing O (log  1.5 (ε n )/ε) items that can (1 ± ε)-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. 
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  2. 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. 
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  3. 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. 
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  6. 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. 
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