On the Estimation of Missing Data in Incomplete Databases: Autoregressive Bayesian Networks

Missing data can be estimated by means of interpo- lation, time series modelling, or exploiting statistically dependent information. The limits of when one approach is preferable to the alternatives have not been explored, but are likely to be a com- promise between a signal autoregressive information, availability of future observations, stationary behaviour and the strength of the dependence with concomitant information. This paper takes a first step towards clarifying dataset characteristics delimiting the realm of application for each technique. In addition, this paper introduces autoregressive Bayesian networks (AR-BN), a variant of Dynamic Bayesian Networks for completing databases which exploits latent variable relations while still benefitting from autoregressive information of the variable being filled. Using AR-BN, new estimated values are calculated using inference in the dynamic model. Our results unveil how the interplay between the variable autoregressive information and the variable relationship to others in the dataset is critical to selecting the optimal data estimation technique. AR-BN appears as a good candidate ensuring a consistent performance across scenarios, datasets and error metrics.

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