Explainable AI-driven evaluation of plant protein rheology using tree-based and Gaussian process machine learning models

Abstract

In this study, we conducted a comparative analysis of the explainability of Decision Tree Regressor (DTR) and Gaussian Process Regressor (GPR) models in predicting the shear stress and viscosity of sesame protein isolate (SPI) systems, employing explainable machine learning (EML) techniques to elucidate complex, nonlinear relationships among processing parameters. SPI samples were processed across pressure levels ranging from 0 to 100 MPa and ion concentration (IC) values from 0 to 200 mM. DTR model accurately predicted shear stress (R² = 0.999), while a GPR model achieved high performance for viscosity prediction (R² = 0.9925). Formally, the modeling task is framed as learning a predicting mapping function $f:R^p\to R$, where $x\in R^p$ denotes the vector of predictors (pressure, IC, shear rate) and $y\in R$ is the target variable (shear stress or viscosity), by minimizing a loss function such as mean squared error. Interpretation of model predictions using SHapley Additive exPlanations (SHAP), permutation importance, and partial dependence analysis revealed that pressure and IC are the most influential factors affecting shear stress and viscosity, with pressure inducing protein conformational changes that impact rheological properties. The shear rate exhibited a lesser direct impact within the systems examined. Partial Dependence Plots (PDPs) from the DTR model revealed strong, nearly linear positive relationships between pressure and shear stress, while the GPR model depicted more nuanced responses, highlighting the models’ differing sensitivities. Variance-Based Sensitivity Indices (VBSIs) further quantified these influences, with pressure and IC showing higher sensitivity scores in the DTR model compared to the GPR model. Permutation importance and SHAP interaction analyses corroborated these results, emphasizing the dominant role of pressure and IC, both independently and interactively, in determining shear stress. In contrast, viscosity predictions were influenced by more distributed and subtle interactions among all features. Employing explainable machine learning techniques enables a comprehensive understanding of feature relevance in complex, nonlinear rheological systems, facilitating the elucidation of viscosity development in sesame protein systems through rheological indices. This approach ensures no bias toward formulation composition and applied pressure, offering valuable insights for optimizing formulation and processing conditions in food applications to enhance the functional properties of SPI-based products.