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We thank the reviewers for their positive feedback on our paper. Rev 2 and 5 asked the difference between LL-LVM and GP-LVM: As noted in lines 65-68 in introduction, both are Gaussian models, but GP-LVM is parameterised by a stationary covariance function rather than by a local neighbour-defined precision matrix which seeks to explicitly preserve local neighbourhood properties. Rev 1 We will add the complexity analysis. An expensive step in the E-step is the inversion of the posterior precision matrices of both x and C (in eq. We will study possible ways to decrease the complexity in future work.