TY - JOUR
T1 - Efficient Irreversible Monte Carlo Samplers
AU - Faizi, Fahim
AU - Deligiannidis, George
AU - Rosta, Edina
PY - 2020/4/14
Y1 - 2020/4/14
N2 - We present here two irreversible Markov chain Monte Carlo algorithms for general discrete state systems. One of the algorithms is based on the random-scan Gibbs sampler for discrete states and the other on its improved version, the Metropolized-Gibbs sampler. The algorithms we present incorporate the lifting framework with skewed detailed balance condition and construct irreversible Markov chains that satisfy the balance condition. We have applied our algorithms to 1D 4-state Potts model. The integrated autocorrelation times for magnetization and energy density indicate a reduction of the dynamical scaling exponent from z ≈ 1 to z ≈ 1/2. In addition, we have generalized an irreversible Metropolis-Hastings algorithm with skewed detailed balance, initially introduced by Turitsyn et al. [ Physica D 2011, 240, 410 ] for the mean field Ising model, to be now readily applicable to classical spin systems in general; application to 1D 4-state Potts model indicate a square root reduction of the mixing time at high temperatures.
AB - We present here two irreversible Markov chain Monte Carlo algorithms for general discrete state systems. One of the algorithms is based on the random-scan Gibbs sampler for discrete states and the other on its improved version, the Metropolized-Gibbs sampler. The algorithms we present incorporate the lifting framework with skewed detailed balance condition and construct irreversible Markov chains that satisfy the balance condition. We have applied our algorithms to 1D 4-state Potts model. The integrated autocorrelation times for magnetization and energy density indicate a reduction of the dynamical scaling exponent from z ≈ 1 to z ≈ 1/2. In addition, we have generalized an irreversible Metropolis-Hastings algorithm with skewed detailed balance, initially introduced by Turitsyn et al. [ Physica D 2011, 240, 410 ] for the mean field Ising model, to be now readily applicable to classical spin systems in general; application to 1D 4-state Potts model indicate a square root reduction of the mixing time at high temperatures.
UR - http://www.scopus.com/inward/record.url?scp=85083544930&partnerID=8YFLogxK
U2 - 10.1021/acs.jctc.9b01135
DO - 10.1021/acs.jctc.9b01135
M3 - Article
C2 - 32097548
AN - SCOPUS:85083544930
SN - 1549-9618
VL - 16
SP - 2124
EP - 2138
JO - Journal of Chemical Theory and Computation
JF - Journal of Chemical Theory and Computation
IS - 4
ER -