(337d) Uncertainty Propagation for Probabilistic Prediction in Partial Least Squares Using Bootstrap Methods

Partial Least Squares (PLS) is an important modeling technique within pharmaceutical manufacturing that is able to both predict the output space and describe a significant portion of the variance of the input space, through projection on a latent space. This allows PLS to perform well in situations with large numbers of highly correlated input variables. Unfortunately, the latent space found by PLS is non-linearly dependant on the output variables of the training data [1] - a feature that vastly complicates any probabilistic analysis of the errors associated with the technique. This work presents a novel method, based on bootstrapping [2], for calculating a probabilistic output from PLS that automatically takes into consideration the aforementioned non-linearities in the parameter uncertainty.

The main result of this work is a novel probabilistic prediction from PLS, which we demonstrate can differ significantly from predictions that avoid dealing with the non-linear dependence of the predictions on the training data's observed outputs. The benefit of these probabilistic predictions are demonstrated in design space identification. First, we use simulated data to compare our method's performance to those from a perfect model. In addition, we investigate our method's performance on real world data and demonstrate its ability to make predictions that are a reasonable representation of the difference between the model prediction and the true observed data.

[1] Helland, I. S. On the structure of partial least squares regression. Communications in Statistics-Simulation and Computation 17, 581–607 (1988).

[2] Fushiki, T., Komaki, F. & Aihara, K. Nonparametric bootstrap prediction. Bernoulli 11, 293–307 (2005).