Distributional Principal Autoencoders

Understand

Dimension reduction techniques usually lose information in the sense that reconstructed data are not identical to the original data.

• However, we argue that it is possible to have reconstructed data identically distributed as the original data, irrespective of the retained dimension or the specific mapping.
• This can be achieved by learning a distributional model that matches the conditional distribution of data given its low-dimensional latent variables.
• Motivated by this, we propose Distributional Principal Autoencoder (DPA) that consists of an encoder that maps high-dimensional data to low-dimensional latent variables and a decoder that maps the latent variables back to the data space.