Abstract: A method to determine data uncertainty is provided. The method receives a high dimensional data input and a corresponding data output. The method trains a variational autoencoder (VAE) with the high dimensional data input to learn a low dimensional latent space representation of the high dimensional data input. An encoder part of the VAE outputs a set of distributions of the high dimensional dataset in a latent space. The method samples new data samples in the latent space using the set of distributions outputs from the encoder part of the VAE. The method learns a polynomial chaos expansion to map the new data samples in the latent space to the corresponding data output to learn the set of distributions and their relation to perform estimation with high-dimensional dataset under uncertainty such as missing values by estimating the values using the set of distributions.