Abstract 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.

中文翻译：

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似然最大化逆回归：一种新的非线性多元模型

摘要 计算常见的多元回归模型的目的是从 X 观测直接预测校准 y 数据。我们在本文中提出的方法可以解决这个问题。实际上，我们提出了一个回归模型，该模型依赖于通过 X 中预期误差的似然最大化来预测 y。我们将我们的无参数算法命名为似然最大化逆回归 (LMIR)。使用 4 个不同的数据集，我们将 LMIR 性能与偏最小二乘法-1 (PLS1)、非线性 PLS 变体和另一种逆回归方法：切片逆回归 (SIR) 进行了比较。LMIR 在几乎所有研究案例中都产生了更好的验证性能。我们还证明了 LMIR 能够在不创建新模型的情况下考虑验证 X 观测中存在的任何已知和额外噪声，根据 PLS1 和 SIR 的要求。从一种仪器构建的 LMIR 模型可以很容易地转移到另一种仪器上。