Generative adversarial learning for missing data imputation

Missing data widely exist in industrial problems and lead to difficulties in further modeling and analysis. Recently, a number of deep learning methods have been proposed for missing data imputation and have shown promising performance in various scenarios. Nevertheless, the inputs of imputation networks of these methods are usually incomplete data filled with zeros, which means the missing values always affect the output of the network and the network should be sufficiently large to have a strong denoising ability. Thus, these methods may not provide satisfactory imputation when the missing rate is high. In this work, we present a novel method called GANImputer for missing data imputation. The method is based on the generative adversarial network, and the input of the imputation network, namely a generator, is not incomplete data but a low-dimensional latent variable that can be optimized. The optimization process is composed of three stages. First, we optimize a generator via adversarial training. Second, the latent variable is optimized, while the generator is fixed. Finally, we fine-tune the generator and latent variable jointly. To analyze the theoretical mechanism of our GANImputer, we provide a generalization error bound with respect to missing not at random, which is practical and meaningful. Our method is tested on five diverse benchmark datasets and the Tennessee Eastman process and outperforms a few deep learning based imputation methods.