Likelihood Maximization Inverse Regression: A novel non-linear multivariate model

Common multivariate regression models are calculated with the objective of directly predicting calibration y data from X observations. Our proposed methodology, presented in this paper, inverses the problem. Indeed, we propose a regression model which relies on predicting y by the likelihood maximization of expected errors in X. We named our parameter-free algorithm Likelihood Maximization Inverse Regression (LMIR). Using 4 different datasets, we compared LMIR performance with Partial Least Squares-1 (PLS1), a non-linear PLS variant and another inverse regression method: Sliced Inverse Regression (SIR). LMIR yielded better validation performances in almost all study cases. We also demonstrated that LMIR was able to consider any known and additional noise present in validation X observations without creating a new model, as required in PLS1 and SIR. A LMIR model built from one instrument could then be easily transferred to another.