A non-linear partial least squares based on monotonic inner relation.

Area of Science:

• Chemometrics
• Statistical Modeling
• Computational Biology

Background:

• Traditional regression models struggle with complex datasets common in Chinese Medicine (CM) dose-effect research, often exhibiting limited observations, multicollinearity, and nonlinearity.
• Existing Partial Least Squares (PLS) variants have limitations in accurately modeling intricate relationships within such data.

Purpose of the Study:

• To introduce a novel regression model, monotonic inner relation-based non-linear partial least squares (MIR-PLS), designed to overcome the limitations of existing methods for analyzing complex dose-effect relationships.
• To evaluate the performance of MIR-PLS against established PLS variants using diverse datasets.

Main Methods:

• MIR-PLS employs a piecewise mapping function utilizing monotonic cubic splines to capture nonlinear inner relationships between input and output score vectors.
• A novel weight updating strategy (WUS) is integrated, capitalizing on the properties of monotonic functions.
• The model was benchmarked against standard PLS, QPLS, EB-QPLS, NNPLS, and SPL-PLS.

Main Results:

• MIR-PLS demonstrated superior or comparable predictive performance across various datasets, including Chinese Medicine dose-effect relationships and near-infrared (NIR) spectroscopy data.
• The model proved effective in handling datasets with and without significant nonlinear relationships.
• General applicability was observed, indicating robustness beyond the initial application domain.

Conclusions:

• MIR-PLS offers a powerful and versatile tool for regression analysis, particularly for complex datasets with nonlinearities.
• The proposed method enhances the ability to model intricate dose-effect relationships and has broad applicability in scientific research.