Handling incomplete heterogeneous data using VAEs

•Evidence Lower Bound on incomplete datasets, computed only on the observed data, regardless of the pattern of missing data.•Generative model that handles mixed numerical and nominal likelihood models, parametrized using deep neural networks (DNNs).•Stable recognition model that handles incomplete datasets without increasing its complexity or promoting overfitting.•Data-normalization input/output layer prevents a few dimensions of the data dominating the training of the VAE, improving the training convergence.•Comparison with state-of-the-art methods on six datasets for both missing data imputation and predictive tasks.