Reproduce “The Boomerang Sampler” on OpenResearch
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About this paper
Joris Bierkens, Sebastiano Grazzi, Kengo Kamatani, Gareth Roberts
Boomerang addresses costly Bayesian inference by replacing straight-line motion in piecewise-deterministic samplers with elliptical dynamics around a Gaussian reference and target-informed velocity reflections. It adds exact subsampling with control variates and factorisation for sparse dependencies. In fixed-dimension logistic regression, subsampled methods kept ESS per CPU second roughly fixed as data grew, unlike non-subsampled versions; this does not establish universal wall-clock gains.
Key insights
- Utilizing Hamiltonian-like deterministic dynamics generates piecewise elliptical trajectories, which can reduce the number of switching events and potentially improve scaling with dimension compared to constant-velocity PDMC methods.
- Exact subsampling, when combined with a control variate gradient estimator, enables an O(n) computational advantage by preventing the event rate from increasing with the number of observations.
- Factorizing the Boomerang Sampler allows for component-wise updates that efficiently exploit sparse conditional dependencies in high-dimensional models.
Summary by alphaXiv.
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