Cross-Validation for Partial Least Squares Regression Models

Partial Least Squares (PLS) regression is a widely used method for handling high-dimensional data with multicollinearity issues. Cross-validation serves as a critical step in evaluating model prediction performance, while outlier detection helps identify anomalous samples in the dataset, thereby enhancing model robustness.

Implementing cross-validation for PLS regression in MATLAB typically involves the following workflow: First, partition the dataset into multiple subsets using functions like cvpartition. Then iteratively designate one subset as the test set while using the remaining subsets for model training. The model performance is evaluated by calculating the Prediction Residual Error Sum of Squares (PRESS) statistic. The optimal number of principal components is determined based on cross-validation results, often through the plsregress function which supports built-in cross-validation options.

Outlier detection can be implemented by analyzing sample leverage values and residuals. Samples with high leverage values exert significant influence on model parameter estimates, while those with large residuals may violate model assumptions. The MATLAB implementation typically involves calculating Hotelling's T² for leverage and Q-residuals for model errors. Combining these two metrics through functions like robustfit or custom scripts enables effective identification of potential outliers.

Understanding these technical details facilitates the construction of more reliable predictive models, particularly applicable to high-dimensional data analysis in fields such as chemometrics and bioinformatics where PLS regression is commonly implemented using specialized toolboxes like PLS_Toolbox or custom MATLAB scripts.