Involutive MCMC: a Unifying Framework

Name & Citation Appendix Metropolis-Hastings (Hastings, 1970) B.1 Markov Chain Monte Carlo (MCMC) is a computational Mixture Proposal (Habib & Barber, 2018) B.2 approach to fundamental problems such Multiple-Try Metropolis (Liu et al., 2000) B.3 as inference, integration, optimization, and simulation. Sample-Adaptive MCMC (Zhu, 2019) B.4 The field has developed a broad spectrum Reversible-Jump MCMC (Green, 1995) B.5 of algorithms, varying in the way they are motivated, Hybrid Monte Carlo (Duane et al., 1987) B.6 the way they are applied and how efficiently RMHMC (Girolami & Calderhead, 2011) B.7 they sample. Despite all the differences, many of NeuTra (Hoffman et al., 2019) B.8 them share the same core principle, which we A-NICE-MC (Song et al., 2017) B.9 unify as the Involutive MCMC (iMCMC) framework. L2HMC (Levy et al., 2017) B.10 Building upon this, we describe a wide Persistent HMC (Horowitz, 1991) B.11 range of MCMC algorithms in terms of iMCMC, Gibbs (Geman & Geman, 1984) B.12 and formulate a number of "tricks" which one Look Ahead (Sohl-Dickstein et al., 2014) B.13 can use as design principles for developing new NRJ (Gagnon & Doucet, 2019) B.14 MCMC algorithms. Thus, iMCMC provides a Lifted MH (Turitsyn et al., 2011) B.15 unified view of many known MCMC algorithms, which facilitates the derivation of powerful extensions. Table 1: List of algorithms that we describe by the Involutive We demonstrate the latter with two MCMC framework. See their descriptions and formulations examples where we transform known reversible in terms of iMCMC in corresponding appendices.