Supplementary Material " Fast Bayesian Estimation of Point Process Intensity as Function of Covariates "

Current affiliation is Y okohama City University. We detail the derivation of the predictive covariance shown in (19-20). We detail the derivation of the marginal likelihood, p (D), shown in (23). H |. Finally, we obtain the marginal likelihood in a tractable form, log p(D) = log |Z | 1 2 log |I We detail the derivation of the functional determinant of equivalent kernel, |H|, when the naive and degenerate approaches are applied. S4.1 Naive Approach The equivalent kernel is constructed under the naive approach as follows: h( y, y Mercer's theorem [ 5 ] states that the kernel function of finite rank M has a diagonal representation such that k ( y, y S5.1 Model Configuration Augmented Permanental Process (APP) Let the number of samples for quasi-Monte Carlo method be denoted by J, and the ranks of approximate kernel function for Random feature map [ 6 ] and Nyström approximation [ 8, 9 ] be denoted by M We employed a popular gradient descent algorithm, Adam [ 4 ], to perform the minimization problem (see Section 2.2), { ˆ v B was set as 10 in the experiments.