Heterogeneous Multi-output Gaussian Process Prediction
This enables more flexible probabilistic modeling for applications like behavioral studies and demographic data, though it is an incremental extension of existing multi-output Gaussian process methods.
The authors tackled the problem of modeling heterogeneous outputs with different likelihood functions by extending multi-output Gaussian processes, achieving tractable variational inference through conditional independence assumptions and an inducing variable framework.
We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in all likelihoods as latent functions. Our multi-output Gaussian process uses a covariance function with a linear model of coregionalisation form. Assuming conditional independence across the underlying latent functions together with an inducing variable framework, we are able to obtain tractable variational bounds amenable to stochastic variational inference. We illustrate the performance of the model on synthetic data and two real datasets: a human behavioral study and a demographic high-dimensional dataset.