Abstract
Predicting the time at which the integral over a stochastic process reaches a target level is a value of interest in many applications. Often, such computations have to be made at low cost, in real time. As an intuitive example that captures many features of this problem class, we choose progress bars, a ubiquitous element of computer user interfaces. These predictors are usually based on simple point estimators, with no error modelling. This leads to fluctuating behaviour confusing to the user. It also does not provide a distribution prediction (risk values), which are crucial for many other application areas. We construct and empirically evaluate a fast, constant cost algorithm using a Gauss-Markov process model which provides more information to the user.
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Notes
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The expositions in this section could also be formulated more generally (for Matérn-class covariances) in the framework of state-space models and associated filters [11]. The derivations here only work for our specific choice of the Ornstein-Uhlenbeck kernel (the first member of the Matérn class), but they allow a more straightforward treatment of the uncertainty on the parametric mean.
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Dataset available at http://sidekick.epfl.ch/data.
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Kiefel, M., Schuler, C., Hennig, P. (2014). Probabilistic Progress Bars. In: Jiang, X., Hornegger, J., Koch, R. (eds) Pattern Recognition. GCPR 2014. Lecture Notes in Computer Science(), vol 8753. Springer, Cham. https://doi.org/10.1007/978-3-319-11752-2_26
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DOI: https://doi.org/10.1007/978-3-319-11752-2_26
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