Conceptposterior score / ∇x log p(x|y)

Posterior Score

In Bayesian inverse problems, the gradient of the posterior probability density with respect to the data, equal to the sum of the prior score and the likelihood score. It usually cannot be obtained directly because the likelihood term is difficult to compute.

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Nov 3

According to Bayes' theorem, the posterior score equals the prior score plus the likelihood score, i.e., ∇x log p(x|y) = ∇x log p(x) + ∇x log p(y|x).

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According to Bayes' theorem, the posterior score equals the prior score plus the likelihood score, i.e., ∇x log p(x|y) = ∇x log p(x) + ∇x log p(y|x).

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Source Articles

Accelerating Bayesian Posterior Sampling in Diffusion Models: A Review of Offline-Online Trade-offsNov 3