Machine learning methods as a tool to analyse incomplete or irregularly sampled radon time series data

Machine learning is a class of statistical techniques which has proven to be a powerful tool for modelling the behaviour of complex systems, in which response quantities depend on assumed controls or predictors in a complicated way. In this paper, as our first purpose, we propose the application of machine learning to reconstruct incomplete or irregularly sampled data of time series indoor radon (²²²Rn). The physical assumption underlying the modelling is that Rn concentration in the air is controlled by environmental variables such as air temperature and pressure. The algorithms "learn" from complete sections of multivariate series, derive a dependence model and apply it to sections where the controls are available, but not the response (Rn), and in this way complete the Rn series. Three machine learning techniques are applied in this study, namely random forest, its extension called the gradient boosting machine and deep learning. For a comparison, we apply the classical multiple regression in a generalized linear model version. Performance of the models is evaluated through different metrics. The performance of the gradient boosting machine is found to be superior to that of the other techniques. By applying learning machines, we show, as our second purpose, that missing data or periods of Rn series data can be reconstructed and resampled on a regular grid reasonably, if data of appropriate physical controls are available. The techniques also identify to which degree the assumed controls contribute to imputing missing Rn values. Our third purpose, though no less important from the viewpoint of physics, is identifying to which degree physical, in this case environmental variables, are relevant as Rn predictors, or in other words, which predictors explain most of the temporal variability of Rn. We show that variables which contribute most to the Rn series reconstruction, are temperature, relative humidity and day of the year. The first two are physical predictors, while "day of the year" is a statistical proxy or surrogate for missing or unknown predictors.