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Variational Autoencoders (VAEs) have recently been highly successful atimputing and acquiring heterogeneous missing data. However, within thisspecific application domain, existing VAE methods are restricted by using onlyone layer of latent variables and strictly Gaussian posterior approximations.To address these limitations, we present HH-VAEM, a Hierarchical VAE model formixed-type incomplete data that uses Hamiltonian Monte Carlo with automatichyper-parameter tuning for improved approximate inference. Our experiments showthat HH-VAEM outperforms existing baselines in the tasks of missing dataimputation and supervised learning with missing features. Finally, we alsopresent a sampling-based approach for efficiently computing the informationgain when missing features are to be acquired with HH-VAEM. Our experimentsshow that this sampling-based approach is superior to alternatives based onGaussian approximations.

Missing Data Imputation and Acquisition with Deep Hierarchical Models and Hamiltonian Monte Carlo