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The parameters δ W and δ H in the MRF models can be estimated using standard marginalization procedures or by maximizing the Type II ML estimate for (10).
Here, we describe the procedure only for submodules; for modules, the only difference is that it is first necessary to compute module-to-gene-set and module-to-gene probabilities by standard marginalization.
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One can express ℒ(c) by marginalization, (11) where is the standard likelihood function for model (7) given and, with varying over all possible values of, and is determined by the prior (10).
Following the standard GP regression methodology [ 118], the marginalization is done over the latent regression function and the hyperparameters are estimated using type II maximum likelihood estimation with a conjugate gradient based optimization algorithm initiated with ten randomly chosen hyperparameter values.
where the first term corresponds to the standard Gaussian case, and the second is a marginalization of the noise term over the last available distribution (i.e., we write n k (ϕ k ) to explicitly emphasize the dependency on the noise latent variables, ϕ k ).
When colleges, our main centers of intellectual culture, lower standards of academic excellence in order to increase standards of athletic excellence, they implicitly support the popular marginalization of the intellectual enterprise.
To be a brown girl anywhere in the world, let alone in America, is to experience exclusion and marginalization from mainstream media, and from mainstream beauty standards.
8. Phyllis Rooney has argued that compared with other recently developed approaches that challenge some of the standard assumptions of mainstream epistemology, feminist epistemology suffers a greater degree of marginalization from what she calls "epistemology proper"(Rooney 2011).
More research is needed to examine the relationship of perceived invisibility to marginalization, whether invisibility is a byproduct of being marginalized or part of the marginalization process itself.
The method incorporates a parallel marginalization (PMMC) step in conjunction with the hybrid Monte Carlo (HMC) scheme to improve samples generated by standard particle filters.
"That's not marginalization.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com