Multi-Target Tobit Models for Completing Water Quality Data

Monitoring microbiological behaviors in water is crucial to manage public health risk from waterborne pathogens, although quantifying the concentrations of microbiological organisms in water is still challenging because concentrations of many pathogens in water samples may often be below the quantification limit, producing censoring data. To enable statistical analysis based on quantitative values, the true values of non-detected measurements are required to be estimated with high precision. Tobit model is a well-known linear regression model for analyzing censored data. One drawback of the Tobit model is that only the target variable is allowed to be censored. In this study, we devised a novel extension of the classical Tobit model, called the \emph{multi-target Tobit model}, to handle multiple censored variables simultaneously by introducing multiple target variables. For fitting the new model, a numerical stable optimization algorithm was developed based on elaborate theories. Experiments conducted using several real-world water quality datasets provided an evidence that estimating multiple columns jointly gains a great advantage over estimating them separately.