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Scalability of the inducing‑point variational HMC approach for Gaussian processes

Ascertain the scalability of the inducing‑point variational Hamiltonian Monte Carlo method of Hensman et al. (2015) as the number of Gaussian processes increases and as the dimensionality of the Gaussian processes grows.

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Background

Hensman et al. proposed a variational approximation using inducing points sampled with HMC to handle non‑Gaussian likelihoods, offering an alternative to exact GP inference.

The authors note that, beyond the approximation bias, a key unresolved issue is whether this approach scales effectively with more GPs and higher GP dimensionality, which is critical for complex hierarchical models.

References

Their method, however, is variational and not guaranteed to describe the posterior precisely, and its scalability with increasing numbers or dimensions of GPs remains unclear.

— Fast Riemannian-manifold Hamiltonian Monte Carlo for hierarchical Gaussian-process models (2511.06407 - Hayakawa et al., 9 Nov 2025) in Section 1 (Introduction)