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13 Feb 2023: In Section 3, we review GPs and explainGPTS and ARGP. Learning via hyper-parameter op-timization is explained in Section 4.

13 Feb 2023: may be updated in O(K2) time. However, the remain-ing matrix products require O(N 2K) and O(N 2D) op-erations respectively.

27 Jan 2023: P Q R STU V WX Y. 9. AB C D EF G H IJK L M N OP Q R S TU V W X Y.

13 Feb 2023: q(xK1; xK , θ′, y) TK1(xK1; xK , θ′, θ̂(y)). q(x1; x2, θ′, y) T1(x1; x2, θ′, θ̂(y)) ,. (16). where Tk are the corresponding reverse transition ... This simulates an ideal casewhere the energy levels are close, or the transition op-erators

13 Feb 2023: Boyd, Stephen and Vandenberghe, Lieven. Convex Op-timization. Cambridge University Press, New York,NY, USA, 2004.

13 Feb 2023: directededge. This association is represented by the covarianceof ǫp and ǫj, vpj.

13 Feb 2023: As seen in Equation 9, in SHGP the base weights of boththe nodes i and j contribute to the edge weight Jij, as op-posed to the HGP where only one

13 Feb 2023: Blei et al. (2005) de-scribe a variational Bayesian (VB) approach which op-timizes a lower bound on the marginal likelihood of aDPM and they compare it thoroughly with standardMCMC methods

27 Jan 2023: This association is represented by thecovariance of ǫp and ǫj , vpj.

13 Feb 2023: In our experiments, we use simplereparameterizations of model parameters that allow our op-timizers to work with arbitrary values.