Researchers Develop A Novel Multilinear Predictive Modeling Method


Two researchers hailing from Wageningen University and the Norwegian University of Life Sciences collaborated on a new method that improves on existing multilinear predictive modeling methods.

A breakthrough in multilinear predictive modeling has been unveiled by researchers at Wageningen University and Research and the Norwegian University of Life Sciences, according to a recent study published in the Journal of Chemometrics (1).

Multilinear predictive modeling is a statistical method commonly used in chemometric analysis. It examines multiple independent variables against a dependent variable and the relationship between them. It has been applied across the physical science fields (3–8). Because chemometrics handles data generated by advanced analytical instruments, multilinear predictive modeling methods are essential to interpret the higher order data (1).

Traditional multilinear regression approaches are often inadequate for this type of analysis because of the complexity of the data structures. As a result, lead author Puneet Mishra, in collaboration with contributor Kristian Hovde Liland, proposed a new method designed to extract multilinear information inherent in the data, which is typically lost when analyzed in unfolded form (1). Their study demonstrated that their method could handle outlier observations, which improves the accuracy of predictive models.

Digital cyberspace with particles and Digital data network connections concept. | Image Credit: © KanawatTH -

Digital cyberspace with particles and Digital data network connections concept. | Image Credit: © KanawatTH -

The main feature of this approach is in its iterative down-weighting of outlier observations in both the predictor and response space (1). Traditional methods require separate outlier removal analysis. However, Mishra and Liland’s method overcomes this issue by integrating outlier handling into the modeling process (1). The result is that time and computational resources are saved.

The effectiveness of the method was demonstrated through extensive testing on three real multilinear data sets. In each case, the new approach outperformed traditional N-way partial least squares (NPLS) modeling in terms of root mean squared error of prediction (1).

Moreover, the versatility of the proposed algorithm extends beyond outlier handling. By adjusting a single parameter, it can seamlessly transition between robust multilinear modeling, traditional PLS analysis, and even iterative robust PLS (irPLS) analysis (1).

As a result, the researchers demonstrated in their study that this method improves multilinear predictive modeling for chemometrics. Because of their modifications to their method, Mishra and Liland show its effectiveness in improving the accuracy of statistical predictions and its efficiency by automating the outlier handling process.

By empowering researchers to effectively model complex data structures, the method proposed by Mishra and Liland holds the potential to accelerate discoveries and advancements across various domains of science and industry.


(1) Mishra, P.; Liland, K. H. Iterative Re-weighted Multilinear Partial Least Squares Modelling for Robust Predictive Modelling. J. Chemom. 2023, ASAP. DOI: 10.1002/cem.3527

(2) Allen, A. E. A.; Tkatchenko, A. Machine Learning of Material Properties: Predictive and Interpretable Multilinear Models. Sci. Adv. 2022, 8 (18). DOI: 10.1126/sciadv.abm.7185

(3) Isayev, O.; Oses, C.; Toher, C.; et al. Universal Fragment Descriptors for Predicting Properties of Inorganic Crystals. Nat. Commun. 2017, 8, 15679. DOI: 10.1038/ncomms15679

(4) Xie, T.; Grossman, J. C. Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties. Phys. Rev. Lett. 2018, 120, 145301. DOI: 10.1103/PhysRevLett.120.145301

(5) Mikulskis, P.; Alexander, M. R.; Winkler, D. A. Toward Interpretable Machine Learning Models for Materials Discovery. Adv. Intell. Syst. 2019, 1, 1900045. DOI: 10.1002/aisy.201900045

(6) Pilania, G. Machine Learning in Materials Science: From Explainable Predictions to Autonomous Design. Comput. Mater. Sci. 2021, 193, 110360. DOI: 10.1016/j.commatsci.2021.110360

(7) Ouyang, R.; Curtarolo, S.; E. Ahmetcik, E.; et al. SISSO: A Compressed-Sensing Method for Identifying the Best Low-Dimensional Descriptor in an Immensity of Offered Candidates. Phys. Rev. Mater. 2018, 2, 083802. DOI: 10.1103/PhysRevMaterials.2.083802

(8) Jha, D.; Ward, L.; Paul, A.; et al. ElemNet: Deep Learning the Chemistry of Materials from Only Elemental Composition. Sci. Rep. 2018, 8, 17593. DOI: 10.1038/s41598-018-35934-y

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