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    A new quantile tracking algorithm using a generalized exponentially weighted average of observations

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    Type
    Article
    Authors
    Hammer, Hugo Lewi cc
    Yazidi, Anis
    Rue, Haavard cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2018-11-10
    Permanent link to this record
    http://hdl.handle.net/10754/630030
    
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    Abstract
    The Exponentially Weighted Average (EWA) of observations is known to be a state-of-art estimator for tracking expectations of dynamically varying data stream distributions. However, how to devise an EWA estimator to track quantiles of data stream distributions is not obvious. In this paper, we present a lightweight quantile estimator using a generalized form of the EWA. To the best of our knowledge, this work represents the first reported quantile estimator of this form in the literature. An appealing property of the estimator is that the update step size is adjusted online proportionally to the difference between current observation and the current quantile estimate. Thus, if the estimator is off-track compared to the data stream, large steps will be taken to promptly get the estimator back on-track. The convergence of the estimator to the true quantile is proven using the theory of stochastic learning. Extensive experimental results using both synthetic and real-life data show that our estimator clearly outperforms legacy state-of-the-art quantile tracking estimators and achieves faster adaptivity in dynamic environments. The quantile estimator was further tested on real-life data where the objective is efficient in online control of indoor climate. We show that the estimator can be incorporated into a concept drift detector to efficiently decide when a machine learning model used to predict future indoor temperature should be retrained/updated.
    Citation
    Hammer HL, Yazidi A, Rue H (2018) A new quantile tracking algorithm using a generalized exponentially weighted average of observations. Applied Intelligence. Available: http://dx.doi.org/10.1007/s10489-018-1335-7.
    Publisher
    Springer Nature
    Journal
    Applied Intelligence
    DOI
    10.1007/s10489-018-1335-7
    Additional Links
    http://link.springer.com/article/10.1007/s10489-018-1335-7
    ae974a485f413a2113503eed53cd6c53
    10.1007/s10489-018-1335-7
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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