Simulatenous Estimation of Categorical and Continuous Variables with DeepKriging
摘要
Accurately modeling continuous and categorical variables in geoscience problems is challenging due to their distinct statistical properties and strong spatial interdependencies. This work modified a deep neural network framework (conditioned deepkriging, C-DK) to jointly/simultaneously model categorical and continuous variables. The C-DKCont+Cat estimates both continuous variables and categorical probabilities from a single input set, ensuring that the probabilities are non-negative and sum-to-one without the need for constraints or post-processing. The C-DKGeo integrates exhaustive geological information by unifying spatial Euclidean and categorical distances, thereby reducing labor-intensive preprocessing. Spatial dependencies are embedded via kernel basis functions and considers locally dependent moments to exactly reproduce observed data at sampled locations. Across multiple datasets, C-DKCont+Cat achieves estimation accuracy on par with ordinary kriging (OK) and indicator kriging, while the C-DKGeo improves R2 by up to 6% compared to domain-based OK. In addition to delivering competitive accuracy and better integration of complex geological data types, the proposed methods simplify implementation as they require minimal preprocessing, streamline parameter inference, relax assumptions on distributions and stationarity, easily consider multiple categories, and automate hyperparameter tuning. Overall, the proposed models offer flexible, data-driven alternatives to traditional geostatistical techniques for spatial estimation in geospatial applications.