In the present thesis a broad spectrum of high dimensional problems with application to healthcare will be explored. We shall review the state-of-the-art methods that are employed when trying to detect genetic factors that affect gene expression, which is a core problem in genetics. We shall also present two popular classes of generative models, namely Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) and their variants. Subsequently, we shall review some new developed imputation methods which are based on GANs and VAEs. We shall assess their performance under various missingness scenarios via accordingly designed experiments and simulation studies. We shall proceed via introducing our method on GANs’ inversion and evaluate its performance in a newly suggested manner. Finally, we shall conclude this thesis with our main findings and future work.