In a variety of disciplines such as social sciences, psychology, medicine and
economics, the recorded data are considered to be noisy measurements of latent
variables connected by some causal structure. This corresponds to a family of
graphical models known as the structural equation model with latent variables.
While linear non-Gaussian variants have been well-studied, inference in
nonparametric structural equation models is still underdeveloped. We introduce
a sparse Gaussian process parameterization that defines a non-linear structure
connecting latent variables, unlike common formulations of Gaussian process
latent variable models. The sparse parameterization is given a full Bayesian
treatment without compromising Markov chain Monte Carlo efficiency. We compare
the stability of the sampling procedure and the predictive ability of the model
against the current practice.Comment: 12 pages, 6 figure