Accelerating MCMC algorithms through Bayesian Deep Networks
This work offers an incremental improvement for researchers and practitioners using MCMC algorithms in high-dimensional settings, particularly in fields like cosmology, by speeding up convergence.
This paper addresses the computational cost of MCMC algorithms in high-dimensional distributions by proposing an adaptive MCMC approach that uses Bayesian Neural Network outcomes as the initial proposal. This method increases the acceptance rate in the Metropolis-Hasting algorithm and accelerates MCMC convergence while maintaining accuracy.
Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their versatility in sampling from complicated probability distributions. However, as the dimension of the distribution gets larger, the computational costs for a satisfactory exploration of the sampling space become challenging. Adaptive MCMC methods employing a choice of proposal distribution can address this issue speeding up the convergence. In this paper we show an alternative way of performing adaptive MCMC, by using the outcome of Bayesian Neural Networks as the initial proposal for the Markov Chain. This combined approach increases the acceptance rate in the Metropolis-Hasting algorithm and accelerate the convergence of the MCMC while reaching the same final accuracy. Finally, we demonstrate the main advantages of this approach by constraining the cosmological parameters directly from Cosmic Microwave Background maps.