Variational Bayes on Manifolds
Date: 17 June 2021, Thursday
Time: 12pm AEDT
Contact the organizer: Andriy Olenko a.olenko@latrobe.edu.au
Speaker: A/Prof Minh-Ngoc Tran (University of Sydney)
Abstract:
Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics and machine learning. Nonetheless, the development of the existing VB algorithms is so far generally restricted to the case where the variational parameter space is Euclidean, which hinders the potential broad application of VB methods. This paper extends the scope of VB to the case where the variational parameter space is a Riemannian manifold. We develop an efficient manifold-based VB algorithm that exploits both the geometric structure of the constraint parameter space and the information geometry of the manifold of VB approximating probability distributions. Our algorithm is provably convergent and achieves a decent convergence rate. We develop in particular several manifold VB algorithms including Manifold Gaussian VB and Stiefel Neural Network VB, and demonstrate through numerical experiments that the proposed algorithms are stable, less sensitive to initialization and compares favourably to existing VB methods. This is a joint work with Dang Nguyen and Duy Nguyen.
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