Cross-validation of component models: a critical look at current methods.

Area of Science:

• Statistics
• Machine Learning
• Data Analysis

Background:

• Cross-validation is a standard technique in regression for model selection and error estimation.
• Its application to component models like Principal Component Analysis (PCA) is less standardized.
• Current PCA cross-validation methods often violate the independence of predictions from the predicted components.

Purpose of the Study:

• To review commonly used generic cross-validation schemes for Principal Component Analysis (PCA).
• To assess the performance and validity of these PCA cross-validation methods across various scenarios.
• To highlight the importance of independent predictions in PCA cross-validation.

Main Methods:

• Literature review of existing generic PCA cross-validation techniques.
• Assessment of these methods' adherence to the principle of independent predictions.
• Empirical evaluation of method performance in diverse analytical contexts.

Main Results:

• Most current PCA cross-validation implementations do not guarantee prediction independence.
• The reviewed methods exhibit varying degrees of effectiveness depending on the specific scenario.
• A lack of thorough literature review on PCA cross-validation has been identified.

Conclusions:

• Existing generic cross-validation schemes for PCA require careful scrutiny due to potential violations of independence.
• Further research and standardized practices are needed for reliable PCA cross-validation.
• Selecting appropriate PCA cross-validation methods is crucial for accurate model evaluation and feature selection.