Fast variable selection makes scalable Gaussian process BSS-ANOVA a speedy and accurate choice for tabular and time series regression

The paper explicitly states the Gibbs full conditionals for β, σ^2, and τ^2 (its eqs. (10)–(15)), matching the model’s derivations, including the (P−1)/2 shape for τ^2 when the intercept is unpenalized . It also claims O(NP) training and O(P) per-point prediction in the abstract and notes empirically that the rate-limiting step is constructing X in O(NP) time . For forward selection, the paper presents the algorithm and its tol-based stopping rule but provides no formal halting proof; it simply says the algorithm returns the optimum model . The model supplies a clean termination argument under a finite truncation P, which closes this gap. However, the model also asserts that X^T X is block-diagonal (hence accumulable in O(NP)) due to basis orthogonality; this structural claim is not supported in the paper and generally requires stronger assumptions (orthogonality with respect to the empirical design), so that part is incomplete. Overall: the paper omits a formal halting proof and some parameterization clarifications, while the model adds them but introduces an unsupported structural assumption about X^T X.