Quasi-site-specific probabilistic prediction of clay compression index with limited site data using SSM-NGBayes model

Clay data are typically multivariate, uncertain, site-unique, sparse, and potentially anomalous. These induce great challenges to data-driven clay compression index (Cc) prediction. To overcome these challenges, outlier detection by subsample scoring method (SSM), generic data learning by Natural Gradient Boosting (NGBoost) and site data learning by Bayesian approach are integrated in this study for quasi-site-specific probabilistic prediction of Cc. In this methodology, SSM divides the clay data into univariate, bivariate and multivariate subspaces and constructs corresponding subsamples, then three base detectors are employed for subsample outlier detection and the obtained scores are collectively used to identify outlier samples. Afterwards, NGBoost-based probabilistic model is established by learning from the generic data, and its hyperparameters are optimised using a novel prediction interval-oriented objective function. The NGBoost model predictions on the site data are then served as prior information about Cc. Finally, the Bayesian approach is adopted to produce posterior prediction of Cc based on the prior information and the observed site data. This prior-posterior prediction model named NGBayes model is validated on a global clay dataset. Results show that the proposed SSM is more robust than traditional multivariate outlier detection methods by considering additional spaces. The prior knowledge learned by the NGBoost model is highly informative, and it outperforms other probabilistic machine learning models in both mean prediction accuracy and prediction interval quality. Moreover, the proposed SSM-NGBayes prediction model exhibits satisfactory performance on various sites with limited data.