Handling the Positive-Definite Constraint in the Bayesian Learning Rule

Jul 12, 2020

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Bayesian learning rule is a recently proposed variational inference method, which not only contains many existing learning algorithms as special cases but also enables the design of new algorithms. Unfortunately, when posterior parameters lie in an open constraint set, the rule may not satisfy the constraints and require line-searches which could slow down the algorithm. In this paper, we fix this issue for the positive-definite constraint by proposing an improved rule that naturally handles the constraint. Our modification is obtained using Riemannian gradient methods, and is valid when the approximation attains a block-coordinate natural parameterization (e.g., Gaussian distributions and their mixtures). Our method outperforms existing methods without any significant increase in computation. Our work makes it easier to apply the learning rule in presence of positive-definite constraints in parameter spaces.

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About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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