Zero Variance Differential Geometric Markov Chain Monte Carlo Algorithms

By Theodore Papamarkou, Antonietta Mira, Mark A. Girolami. 2014

37 citations recorded by the source corpus.

Differential geometric Markov Chain Monte Carlo (MCMC) strategies exploit the geometry of the target to achieve convergence in fewer MCMC iterations at the cost of increased computing time for each of the iterations. Such computational complexity is regarded as a potential shortcoming of geometric MCMC in practice. This paper suggests that part of the additional computing required by Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms produces elements that allow concurrent implementation of the zero variance reduction technique for MCMC estimation. Therefore, zero variance geometric MCMC emerges as an inherently unified sampling scheme, in the sense that variance reduction and geometric exploitation of the parameter space can be performed simultaneously without exceeding the computational requirements posed by the geometric MCMC scheme alone. A MATLAB package is provided, which implements a generic code framework of the combined methodology for a range of models.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Control functionals for Monte Carlo integration (2014, background): “Gradient information is thus precomputed in the sampling scheme and can be leveraged ‘for free’, as noted by Papamarkou et al. (2014).”
The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation (2016, methodology): “The methodology applies whenever the gradient of the log-likelihood (and the log-prior) can be evaluated and therefore can be used “for free” when differential geometric sampling schemes are employed in construction of the Markov chain (Papamarkou, Mira, and Girolami 2014).”
Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods (2014, background): “Further support for the use of the score as a control variate was provided in Papamarkou et al. (2014); Oates et al. (2015), who demonstrated that the approach ﬁts naturally within Hamiltonian-type and Langevin-type MCMC schemes that themselves make use of the score, requiring essentially no…”
The Controlled Thermodynamic Integral for Bayesian Model Comparison (2014, methodology): “The methodology applies whenever the gradient of the log-likelihood (and the log-prior) can be evaluated and therefore can be used “for free” when differential geometric sampling schemes are employed in construction of the Markov chain (Papamarkou et al., 2014).”