Manifold Gaussian Variational Bayes on the Precision Matrix
arxiv(2022)
摘要
We propose an optimization algorithm for Variational Inference (VI) in
complex models. Our approach relies on natural gradient updates where the
variational space is a Riemann manifold. We develop an efficient algorithm for
Gaussian Variational Inference whose updates satisfy the positive definite
constraint on the variational covariance matrix. Our Manifold Gaussian
Variational Bayes on the Precision matrix (MGVBP) solution provides simple
update rules, is straightforward to implement, and the use of the precision
matrix parametrization has a significant computational advantage. Due to its
black-box nature, MGVBP stands as a ready-to-use solution for VI in complex
models. Over five datasets, we empirically validate our feasible approach on
different statistical and econometric models, discussing its performance with
respect to baseline methods.
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