Spatial multivariate data imputation using deep learning and lambda distribution

Artificial neural networks (ANNs) are often used to establish a mapping between an input data set and a corresponding output. There are many applications that rely on quantifying the conditional distribution of the output given the input data set. This is often referred to as aleatoric uncertainty associated with variability of the outcome due to inherently random effects. In this paper, deep learning is used to quantify moments of the conditional distribution of a missing variable based on homotopic multivariate observations. The lambda distribution is then used to parametrize the conditional distribution based on the provided moments. Geostatistical quantification of spatial continuity complements the multivariate conditional distribution through Bayesian updating to inform multiple data imputation that accounts for the uncertainty associated with the missing variable(s). Geological data are often incomplete, and data imputation is an essential step to avoid excluding heterotopic data. The proposed data imputation framework trains multi layer perceptron (MLP) neural networks to characterize multivariate relationships inferred from homotopic training data. A case study is conducted using geological data from a lateritic Nickle deposit to demonstrate application of the proposed methodology.