Interval predictor model

In regression analysis, an interval predictor model (IPM) is an approach to regression where bounds on the function to be approximated are obtained. This differs from other techniques in machine learning, where usually one wishes to estimate point values or an entire probability distribution. Interval Predictor Models are sometimes referred to as a nonparametric regression technique, because a potentially infinite set of functions are contained by the IPM, and no specific distribution is implied for the regressed variables.

Multiple-input multiple-output IPMs for multi-point data commonly used to represent functions have been recently developed.[1] These IPM prescribe the parameters of the model as a path-connected, semi-algebraic set using sliced-normal [2] or sliced-exponential distributions.[3] A key advantage of this approach is its ability to characterize complex parameter dependencies to varying fidelity levels. This practice enables the analyst to adjust the desired level of conservatism in the prediction.

As a consequence of the theory of scenario optimization, in many cases rigorous predictions can be made regarding the performance of the model at test time.[4] Hence an interval predictor model can be seen as a guaranteed bound on quantile regression. Interval predictor models can also be seen as a way to prescribe the support of random predictor models, of which a Gaussian process is a specific case .[5]

  1. ^ Crespo, Luis G.; Kenny, Sean P.; Colbert, Brendon K.; Slagel, Tanner (2021). "Interval Predictor Models for Robust System Identification". 2021 60th IEEE Conference on Decision and Control (CDC). pp. 872–879. doi:10.1109/CDC45484.2021.9683582. ISBN 978-1-6654-3659-5. S2CID 246479771.
  2. ^ Crespo, Luis; Colbert, Brendon; Kenny, Sean; Giesy, Daniel (2019). "On the quantification of aleatory and epistemic uncertainty using Sliced-Normal distributions". Systems and Control Letters. 34: 104560. doi:10.1016/j.sysconle.2019.104560. S2CID 209339118.
  3. ^ Crespo, Luis G.; Colbert, Brendon K.; Slager, Tanner; Kenny, Sean P. (2021). "Robust Estimation of Sliced-Exponential Distributions⋆". 2021 60th IEEE Conference on Decision and Control (CDC). pp. 6742–6748. doi:10.1109/CDC45484.2021.9683584. ISBN 978-1-6654-3659-5. S2CID 246476974.
  4. ^ Campi, M.C.; Calafiore, G.; Garatti, S. (2009). "Interval predictor models: Identification and reliability". Automatica. 45 (2): 382–392. doi:10.1016/j.automatica.2008.09.004. ISSN 0005-1098.
  5. ^ Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P. (2018). "Staircase predictor models for reliability and risk analysis". Structural Safety. 75: 35–44. doi:10.1016/j.strusafe.2018.05.002. ISSN 0167-4730. S2CID 126167977.