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About this paper
Vincent Adam
The paper presents VCGP, a sparse variational method for regression with multiple latent Gaussian-process functions. It places their inducing-point values in one joint Gaussian posterior, allowing cross-function dependence. In a conjugate additive-regression test, VCGP recovered correlation −0.9265, near exact −0.9306, while mean-field gave zero. This toy result does not establish better accuracy or speed.
Key insights
- Explicitly modeling the joint covariance among inducing variables from different latent GPs is crucial for capturing accurate posterior dependencies and correlations that mean-field approaches ignore.
- While mean-field approximations can achieve similar predictive accuracy for posterior means, they fundamentally fail to provide reliable uncertainty estimates for combinations of coupled latent functions.
- The VCGP approach successfully combines the scalability benefits of sparse GP approximations (linear scaling with data points N) with the improved accuracy of structured variational posteriors, albeit with higher polynomial complexity in the number of inducing points (M) and latent GPs (C).
Summary by alphaXiv.
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