## 1 Introduction
The stacking ensemble learning model established in this article trains primary learners on the first-layer basic model through k-fold cross-validation and selects a model with strong generalization ability in the second layer to correct the learning of multiple basic learners in the first layer deviation. Moreover, none of the data blocks predicted by the primary learner participate in the training of the learner, so that all data is used only once during model training, thereby reducing the occurrence of overfitting and avoiding model deviation caused by a single algorithm. [PERSON] defines an outlier as \"an observation that deviates so much from other observations that it arouses suspicion that it is caused by a different mechanism [24].\" Outliers will adversely affect the fitting of the regression model, thereby making relevant statistical inferences invalid. Therefore, it is very important to perform outlier detection in the dataset [25]. Abnormalities and process fluctuations also occur in normal processes during operation. In actual industrial production, with continuous production of data in the manufacturing process, abnormal data values and data fluctuations are inevitable, and noise is common. In addition, the processing conditions of high-dimensional, small-sample processing methods are more complex and changeable, and abnormal data outliers and equipment offset errors often occur. These factors cause the machine learning process to be affected by abnormal values and affect the final quality prediction effect. In this work, we propose an outlier replacement method based on box graph technology and MICE [26; 27]. This method is not affected by data types and has little influence on the overall distribution of data. Then, ordinary least squares (OLS) is used to identify the abnormal points (strong influence points) of the original data correction, integrating the four methods of studentized residual [28], leverage [29], Cook's distance [30], and DF-FITS [31] to determine abnormal samples. In the feature-engineering stage, the CatBoost algorithm is used to construct combination features, and strong combination features are selected as new features to construct new feature sets. In order to improve the prediction ability of machine learning, Box-Cox [32] was used to normalize features. To ensure the generalization of the established model, the data features are not reduced in dimension. This paper studies the machine learning regression prediction model of various types of cutting-edge algorithms as the base learning model and establishes a high-dimensional, small-sample stacking ensemble learning [33] regression prediction model for high-dimensional, small-sample industrial production. The MIC [34] was used to calculate the error correlation degree and screen the base model with large difference degree, and it makes the best use of the different observations of data in different models, and also avoids the repeated learning of similar models, leading to the occurrence of overfitting. According to the stacking model framework-based learning mode, the parameters are selected by the combination of random search and grid search algorithm [35]. The minimum correlation stacking ensemble learning regression quality prediction model is constructed. The goals and contributions of this article are (i) in the Industry 4.0 era, it has become easy to obtain high-dimensional multivariate data, and the number of samples may be limited, and a theoretical framework is proposed for industrial product quality prediction in high-dimensional and small-sample scenarios; (ii) there are outliers in the data collected in the industrial process, and an outlier processing method combining multiple algorithms is constructed.