Iterative Imputation of Missing Data Using Auto-Encoder Dynamics

Marek Smieja, Maciej Kolomycki, Lukasz Struski, Mateusz Juda, Mário A. T. Figueiredo

Abstract: This paper introduces an approach to missing data imputation based on deep auto-encoder models, adequate to high-dimensional data exhibiting complex dependencies, such as images. The method exploits the properties of the vector field associated to an auto-encoder, which allows to approximate the gradient of the log-density from its reconstruction error, based on which we propose a projected gradient ascent algorithm to obtain the conditionally most probable estimate of the missing values. Our approach does not require any specialized training procedure and can be used together with any auto-encoder model trained on complete data in a classical way. Experiments performed on benchmark datasets show that imputations produced by our model are sharp and realistic.