Gaussian Process Structural Equation Models with Latent Variables

In a variety of disciplines such as social sci- ences, psychology, medicine and economics, the recorded data are considered to be noisy mea- surements of latent variables connected by some causal structure. This corresponds to a fam- ily 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 in- troduce a sparse Gaussian process parameteriza- tion that defines a non-linear structure connect- ing 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 stabil- ity of the sampling procedure and the predictive ability of the model against the current practice.