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.
[5] Typically the interval predictor model is created by specifying a parametric function, which is usually chosen to be the product of a parameter vector and a basis.
Ellipsoidal parameters sets were used by Campi (2009), which yield a convex optimization program to train the IPM.
[4] Crespo (2016) proposed the use of a hyperrectangular parameter set, which results in a convenient, linear form for the bounds of the IPM.
This enables non-convex IPMs to be created, such as a single layer neural network.
[8] This is achieved by solving the optimisation program where the interval predictor model center line
Sadeghi (2019) demonstrates that the non-convex scenario approach from Campi (2015) can be extended to train deeper neural networks which predict intervals with hetreoscedastic uncertainty on datasets with imprecision.
[10] Crespo (2015) and (2021) applied Interval Predictor Models to the design of space radiation shielding [11] and to system identification.
[12] In Patelli (2017), Faes (2019), and Crespo (2018), Interval Predictor models were applied to the structural reliability analysis problem.
[13] [5] [14] Brandt (2017) applies interval predictor models to fatigue damage estimation of offshore wind turbines jacket substructures.
-regression) belong to a particular class of Interval Predictor Models, for which the reliability is invariant with respect to the distribution of the data.