Abstract In this work, we propose a probabilistic just-in-time (PJIT) modeling methodology with nonlinear feature extraction for estimating quality variables of interest. In literature, deterministic nonlinear feature extraction methods have been employed to deal with high dimensional input data. However, these methods require prespecifying the latent dimensions, which often results in overfitting. To circumvent this issue, we employ the Bayesian Gaussian process latent variable model (BGPLVM) to extract nonlinear latent variables and determine their dimensions automatically. Owing to the probabilistic framework, the proposed approach involves computing the variational distribution of latent variables for the query sample as well as historical samples, and selecting relevant samples based on a distribution measure for building a local Gaussian process model to predict the quality variable. Furthermore, the applicability of the proposed approach to missing data and multi-rate data is discussed. Two case studies are presented to demonstrate the efficacy of the proposed PJIT model.

中文翻译：

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使用贝叶斯非线性特征提取进行非线性建模的概率即时方法

摘要 在这项工作中，我们提出了一种具有非线性特征提取的概率即时 (PJIT) 建模方法，用于估计感兴趣的质量变量。在文献中，确定性非线性特征提取方法已被用于处理高维输入数据。然而，这些方法需要预先指定潜在维度，这通常会导致过度拟合。为了规避这个问题，我们采用贝叶斯高斯过程潜变量模型（BGPLVM）来提取非线性潜变量并自动确定它们的维度。由于概率框架，所提出的方法涉及计算查询样本和历史样本的潜在变量的变分分布，并根据分布度量选择相关样本，以构建局部高斯过程模型来预测质量变量。此外，还讨论了所提出的方法对缺失数据和多速率数据的适用性。提供了两个案例研究来证明所提出的 PJIT 模型的有效性。