Improved Marginal Unbiased Score Expansion (MUSE) via Implicit Differentiation
This work addresses efficiency and usability issues in hierarchical Bayesian inference for researchers and practitioners, representing an incremental improvement to an existing method.
The paper tackled the problem of improving the Marginal Unbiased Score Expansion (MUSE) algorithm for hierarchical Bayesian inference by applying implicit differentiation to boost performance, reduce numerical error, and remove required user-tuning. The result demonstrated speed improvements over Hamiltonian Monte Carlo by factors of up to 397 on test cases, with good approximate marginal posteriors.
We apply the technique of implicit differentiation to boost performance, reduce numerical error, and remove required user-tuning in the Marginal Unbiased Score Expansion (MUSE) algorithm for hierarchical Bayesian inference. We demonstrate these improvements on three representative inference problems: 1) an extended Neal's funnel 2) Bayesian neural networks, and 3) probabilistic principal component analysis. On our particular test cases, MUSE with implicit differentiation is faster than Hamiltonian Monte Carlo by factors of 155, 397, and 5, respectively, or factors of 65, 278, and 1 without implicit differentiation, and yields good approximate marginal posteriors. The Julia and Python MUSE packages have been updated to use implicit differentiation, and can solve problems defined by hand or with any of a number of popular probabilistic programming languages and automatic differentiation backends.