Expectation Propagation for Likelihoods Depending on an Inner Product of Two Multivariate Random Variables

17th International Conference on Artificial Intelligence and Statistics

数学科学;计算机科学

Tomi Peltola Pasi Jyla¨nki Aki Vehtari ; Department of Biomedical Engineering ; Donders Institute for Brain ; Cognition ; Behaviour ; Department of Biomedical Engineering

PID  :  123764

来源: CEUR

【 摘 要 】

We describe how a deterministic Gaussian posterior approximation can be constructed using expectation propagation (EP) for mod els, where the likelihood function depends on an inner product of two multivariate random variables. The family of applicable models includes a wide variety of important linear latent variable models used in statistical ma chine learning, such as principal component and factor analysis, their linear extensions, and errorsinvariables regression. The EP computations are facilitated by an integral transformation of the Dirac delta function, which allows transforming the multidimen sional integrals over the two multivariate ran dom variables into an analytically tractable form up to onedimensional analytically in tractable integrals that can be efficiently computed numerically. We study the result ing posterior approximations in sparse prin cipal component analysis with Gaussian and probit likelihoods. Comparisons to Gibbs sampling and variational inference are pre