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1. Pseudo-Deterministic Streaming

   https://doi.org/10.4230/LIPIcs.ITCS.2020.79  

   Goldwasser, Shafi ; Grossman, Ofer ; Mohanty, Sidhanth ; Woodruff, David P. ( January 2020 , ITCS)
2. Relative Error Streaming Quantiles

   https://doi.org/10.1145/3452021.3458323  

   Cormode, Graham ; Karnin, Zohar ; Liberty, Edo ; Thaler, Justin ; Veselý, Pavel ( June 2021 , PODS'21: Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems)

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3. Relative Error Streaming Quantiles

   https://doi.org/10.1145/3617891  

   Cormode, Graham ; Karnin, Zohar ; Liberty, Edo ; Thaler, Justin ; Veselý, Pavel ( January 2023 , Journal of the ACM)

   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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4. Relative Error Streaming Quantiles

   https://doi.org/10.1145/3542700.3542717  

   Cormode, Graham ; Karnin, Zohar ; Liberty, Edo ; Thaler, Justin ; Vesely, Pavel ( May 2022 , ACM SIGMOD Record)

   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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5. Streaming Variational Monte Carlo

   https://doi.org/10.1109/TPAMI.2022.3153225  

   Zhao, Yuan ; Nassar, Josue ; Jordan, Ian ; Bugallo, Monica ; Park, Il Memming ( February 2022 , IEEE Transactions on Pattern Analysis and Machine Intelligence)

   Nonlinear state-space models are powerful tools to describe dynamical structures in complex time series. In a streaming setting where data are processed one sample at a time, simultaneous inference of the state and its nonlinear dynamics has posed significant challenges in practice. We develop a novel online learning framework, leveraging variational inference and sequential Monte Carlo, which enables flexible and accurate Bayesian joint filtering. Our method provides an approximation of the filtering posterior which can be made arbitrarily close to the true filtering distribution for a wide class of dynamics models and observation models. Specifically, the proposed framework can efficiently approximate a posterior over the dynamics using sparse Gaussian processes, allowing for an interpretable model of the latent dynamics. Constant time complexity per sample makes our approach amenable to online learning scenarios and suitable for real-time applications. 

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