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Monte Carlo co-ordinate ascent variational inference. (English) Zbl 1447.62030

Summary: In variational inference (VI), coordinate-ascent and gradient-based approaches are two major types of algorithms for approximating difficult-to-compute probability densities. In real-world implementations of complex models, Monte Carlo methods are widely used to estimate expectations in coordinate-ascent approaches and gradients in derivative-driven ones. We discuss a Monte Carlo co-ordinate ascent VI (MC-CAVI) algorithm that makes use of Markov chain Monte Carlo (MCMC) methods in the calculation of expectations required within co-ordinate ascent VI (CAVI). We show that, under regularity conditions, an MC-CAVI recursion will get arbitrarily close to a maximiser of the evidence lower bound with any given high probability. In numerical examples, the performance of MC-CAVI algorithm is compared with that of MCMC and – as a representative of derivative-based VI methods – of Black Box VI (BBVI). We discuss and demonstrate MC-CAVI’s suitability for models with hard constraints in simulated and real examples. We compare MC-CAVI’s performance with that of MCMC in an important complex model used in nuclear magnetic resonance spectroscopy data analysis – BBVI is nearly impossible to be employed in this setting due to the hard constraints involved in the model.

MSC:

62F15 Bayesian inference
62F12 Asymptotic properties of parametric estimators
65C05 Monte Carlo methods
62P35 Applications of statistics to physics

Software:

BATMAN ; PRMLT; ADVI; HMDB; AdaGrad
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