  Clinical patient records are an example of high-dimensional data that is
typically collected from disparate sources and comprises of multiple
likelihoods with noisy as well as missing values. In this work, we propose an
unsupervised generative model that can learn a low-dimensional representation
among the observations in a latent space, while making use of all available
data in a heterogeneous data setting with missing values. We improve upon the
existing Gaussian process latent variable model (GPLVM) by incorporating
multiple likelihoods and deep neural network parameterised back-constraints to
create a non-linear dimensionality reduction technique for heterogeneous data.
In addition, we develop a variational inference method for our model that uses
numerical quadrature. We establish the effectiveness of our model and compare
against existing GPLVM methods on a standard benchmark dataset as well as on
clinical data of Parkinson's disease patients treated at the HUS Helsinki
University Hospital.
