For about a decade, the Machine Intelligence surge has been magnificent. One of the most useful, yet simple tasks performed by Machine Intelligence is Forecasting, which otherwise requires extensive Mathematical Modelling. The point of convergence here, in this research, is on forecasting uniformly probable events. For the same, we would propose an Ensemble Model, that builds on the positives of Recurrent Neural Networks, and the Probability Theory. The key idea behind our proposal is to give priority not only to the forecast by the neural network but also to combine the probability attached to it, and therefore the nomenclature—“Dare Not to avoid the Most Probable Ones”. To initiate the process, 2 parameters, Probabilistic Threshold (k), and Interval Width (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42979_2025_4076_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\lambda $</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>) will be set, followed by breaking down the entire horizon into k intervals of width <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42979_2025_4076_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\lambda $</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>. Each interval will have its probability of being chosen during the forecast, which will be dynamically converged by iterations. Finally, after completion of all the epochs, the step ahead forecast is proposed to be a linear combination of the forecast made by the Recurrent Neural Network subject to the adaption in neuronal weights and biases (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42979_2025_4076_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">$\phi (\text {X})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mtext>X</mtext> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>), and the probability attached with the forecast <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42979_2025_4076_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="142" /> </InlineMediaObject> <EquationSource Format="TEX">$\text {Probability}(\text {Range}_i)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>Probability</mtext> <mo stretchy="false">(</mo> <msub> <mtext>Range</mtext> <mi>i</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. To evaluate the performance of our proposed model, we tested it on several benchmark datasets, like the Airline Passengers dataset, Alcohol Sales dataset, etc., and compared its performance with the state-of-the-art.

Dare Not to Avoid the Most Probable Ones: An Adaptive Probabilistic Interval-Selection Ensemble of Recurrent Neural Networks for Time Series Forecasting

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发表日期：

2025年7月14日

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Anurag Dutta,
K. Lakshmanan,
S. Shanmuga Priya,
R. Karthik,
A. Ramamoorthy

摘要

For about a decade, the Machine Intelligence surge has been magnificent. One of the most useful, yet simple tasks performed by Machine Intelligence is Forecasting, which otherwise requires extensive Mathematical Modelling. The point of convergence here, in this research, is on forecasting uniformly probable events. For the same, we would propose an Ensemble Model, that builds on the positives of Recurrent Neural Networks, and the Probability Theory. The key idea behind our proposal is to give priority not only to the forecast by the neural network but also to combine the probability attached to it, and therefore the nomenclature—“Dare Not to avoid the Most Probable Ones”. To initiate the process, 2 parameters, Probabilistic Threshold (k), and Interval Width ( $\lambda $ $λ$ ) will be set, followed by breaking down the entire horizon into k intervals of width $\lambda $ $λ$ . Each interval will have its probability of being chosen during the forecast, which will be dynamically converged by iterations. Finally, after completion of all the epochs, the step ahead forecast is proposed to be a linear combination of the forecast made by the Recurrent Neural Network subject to the adaption in neuronal weights and biases ( $\phi (\text {X})$ $ϕ (X)$ ), and the probability attached with the forecast $\text {Probability}(\text {Range}_i)$ $Probability ({Range}_{i})$ . To evaluate the performance of our proposed model, we tested it on several benchmark datasets, like the Airline Passengers dataset, Alcohol Sales dataset, etc., and compared its performance with the state-of-the-art.