PLSR建模困惑：LOO验证下RMSEP随成分数增加上升求解

Hey there, this is a super common gotcha when working with datasets where you have way more features than samples—your 20 rows and 480 columns fall squarely into that p >> n category, and that’s the root of your confusing RMSEP trend. Let’s break this down:

Why Your RMSEP Is Rising Instead of Falling #

• Small sample size + high dimensionality = unstable validation: Leave-One-Out (LOO) validation sounds reliable on paper, but with only 20 samples, each "test fold" is just 1 sample, and the training fold still has 19 samples trying to make sense of 480 features. PLSR creates components to explain covariance between features and your target, but once you get past a few components, the model starts fitting noise instead of true signal. LOO’s estimates are wildly variable with tiny samples, so this noise-fitting translates to rising RMSEP until the model can’t extract any more "useless" noise (hence the stabilization at 6 components).
• Weak or absent true signal: If your features don’t have a strong linear relationship with your target variable, even early components might not capture meaningful patterns. Adding more components just makes the model chase random variation in the data, pushing RMSEP up instead of down.

Steps to Fix This & Get More Reliable Results #

• Trim noisy/redundant features first: Start by filtering out features with near-zero variance—they’re only adding noise. You could also use univariate feature selection to keep only features with a significant correlation to your target, or run PCA first to reduce the feature space to a smaller set of meaningful principal components before applying PLSR.
• Switch to a more stable cross-validation method: LOO is too volatile for 20 samples. Try 5-fold cross-validation (each fold has 4 samples) or repeated 5-fold cross-validation (run it 10-20 times and average results) to get a more robust estimate of RMSEP.
• Compare training vs. validation performance: Plot both the training RMSE and validation RMSEP against the number of components. If training RMSE keeps dropping while validation RMSEP rises, that’s a clear sign of overfitting—you should pick the number of components where RMSEP is at its lowest (even if that’s 1 or 2 components, not 6).
• Try regularized PLS variants: Some PLS implementations include L2 regularization (like plsRglm in R or scikit-learn’s PLSRegression with a penalty) which can help prevent overfitting when dealing with high-dimensional, small-sample data.

内容的提问来源于stack exchange，提问作者Rk57