Gaussian Process Structural Equation Models with Latent Variables
This work addresses a bottleneck in fields like social sciences and medicine for modeling causal structures with latent variables, though it appears incremental as it builds on existing nonparametric methods.
The authors tackled the problem of inference in nonparametric structural equation models with latent variables by introducing a sparse Gaussian process parameterization, resulting in improved stability of the sampling procedure and predictive ability compared to current practices.
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.