Pareto Optimal Prediction Intervals with Hypernetworks

Alcántara, Antonio; Galván, Inés María; Aler-Mur, Ricardo

doi:10.1016/j.asoc.2022.109930

Cited by 2 publications

(4 citation statements)

References 24 publications

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“…It should be noted that, instead of a CWC, quality-driven (QD) differentiable criteria could be applied as in work [14]. However, a CWC is more widely used, while QD differentiable criteria demand large batch sizes (50 points and more) for the training to be sustainable, as they utilize the central limit theorem to approximate the binomial distribution during the derivation, which is not often appropriate for various tasks of time series prediction, and should be further studied.…”

Section: Methodsmentioning

confidence: 99%

“…One of the key methods is a non-parametric method for finding lower and upper PI estimates, which has been named LUBE (Lower Upper Bound Estimation) [12,13]. According to the LUBE method, a multi-criteria task is set with conflicting quality criteria, the compromise between which is determined by the Pareto set front, which is sought out via numerical methods [14].…”

Section: Introductionmentioning

confidence: 99%

“…Neural networks are the most used methods [19][20][21] as they can have two outputs that represent the lower and upper bounds of the PIs. Models can be built to directly estimate the lower and upper boundaries of PIs, which can then be narrowed or expanded using optimization methods based on specified quality criteria, using the LUBE method [22][23][24], or by searching for a Pareto compromise [14,25].…”

Section: Introductionmentioning

confidence: 99%

“…Publication [25] suggests dividing the entire training set into two parts and constructing a compromise as a CWC contradiction for two parts of the sample, and then evaluate the results using PICP and PINAW [29,30]. The work [14] presented a methodology for estimating Pareto optimal forecasting intervals using hypernets: POPI-HN. This method can estimate the full set of Pareto optimal solutions for the trade-off between PI coverage and width in regression problems.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Particle Swarm Training of a Neural Network for the Lower Upper Bound Estimation of the Prediction Intervals of Time Series

Gusev,

Chervyakov,

Alexeenko

et al. 2023

Mathematics

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Many time series forecasting applications use ranges rather than point forecasts. Producing forecasts in the form of Prediction Intervals (PIs) is natural, since intervals are an important component of many mathematical models. The LUBE (Lower Upper Bound Estimation) method is aimed at finding ranges based on solving optimization problems taking into account interval width and coverage. Using the Particle Swarm Training of simple neural network, we look for a solution to the optimization problem of the Coverage Width-Based Criterion (CWC), which is the exponential convolution of conflicting criteria PICP (Prediction Interval Coverage Probability) and PINRW (Prediction Interval Normalized Root-mean-square Width). Based on the concept of the Pareto compromise, it is introduced as a Pareto front in the space of specified criteria. The Pareto compromise is constructed as a relationship between conflicting criteria based on the found solution to the optimization problem. The data under consideration are the financial time series of the MOEX closing prices. Our findings reveal that a relatively simple neural network, comprising eight neurons and their corresponding 26 parameters (weights of neuron connections and neuron signal biases), is sufficient to yield reliable PIs for the investigated financial time series. The novelty of our approach lies in the use of a simple network structure (containing fewer than 100 parameters) to construct PIs for a financial time series. Additionally, we offer an experimental construction of the Pareto frontier, formed by the PICP and PINRW criteria.

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Section: Methodsmentioning

confidence: 99%