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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

16 Jul 2024: the constrained op-timization where P is the standard space over which themethod optimizes (P = M′ for MF, P = L for Bethe andTRW), P(xi) is the sub-space constrained to

16 Jul 2024: ReferencesF. Bach. Learning with submodular functions: A convex op-. timization perspective.

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.

13 Feb 2023: One of the main challenges of training mGPs usingneural networks as mapping M is the unwieldy joint op-timization of the parameters θmGP.

13 Feb 2023: We can often exploit this structure to ob-tain a bound on the objective function and proceed by op-timizing this bound.

13 Feb 2023: Hyperparameters of the independent model are op-timized jointly for both processes f A(t) and f B(t) where kernel parameters θKand the global noise variance σ are shared and

13 Feb 2023: Cτ2 ‖W τ‖. 22) with Cτ 0. The op-. timal W τ is therefore the minimizer of the negativelogarithm of (11), which can be obtained by.