An Adaptive Multipath Linear Interpolation Method for Sample Optimization

Yukun Du, Xiao Jin, Hongxia Wang () and Min Lu
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Yukun Du: School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China
Xiao Jin: School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China
Hongxia Wang: School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China
Min Lu: School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China

Mathematics, 2023, vol. 11, issue 3, 1-15

Abstract: When using machine learning methods to make predictions, the problem of small sample sizes or highly noisy observation samples is common. Current mainstream sample expansion methods cannot handle the data noise problem well. We propose a multipath sample expansion method (AMLI) based on the idea of linear interpolation, which mainly solves the problem of insufficient prediction sample size or large error between the observed sample and the actual distribution. The rationale of the AMLI method is to divide the original feature space into several subspaces with equal samples, randomly extract a sample from each subspace as a class, and then perform linear interpolation on the samples in the same class (i.e., K -path linear interpolation). After the AMLI processing, valid samples are greatly expanded, the sample structure is adjusted, and the average noise of the samples is reduced so that the prediction effect of the machine learning model is improved. The hyperparameters of this method have an intuitive explanation and usually require little calibration. We compared the proposed method with a variety of machine learning prediction methods and demonstrated that the AMLI method can significantly improve the prediction result. We also propose an AMLI plus method based on the linear interpolation between classes by combining the idea of AMLI with the clustering method and present theoretical proofs of the effectiveness of the AMLI and AMLI plus methods.

Keywords: multipath; linear interpolation; sample optimization; predicted effects (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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