TY - GEN
T1 - Enhanced Mixture Population Monte Carlo Via Stochastic Optimization and Markov Chain Monte Carlo Sampling
AU - El-Laham, Yousef
AU - Djuric, Petar M.
AU - Bugallo, Monica F.
N1 - Publisher Copyright:
© 2020 IEEE.
PY - 2020/5
Y1 - 2020/5
N2 - The population Monte Carlo (PMC) algorithm is a popular adaptive importance sampling (AIS) method used for approximate computation of intractable integrals. Over the years, many advances have been made in the theory and implementation of PMC schemes. The mixture PMC (M-PMC) algorithm, for instance, optimizes the parameters of a mixture proposal distribution in a way that minimizes that Kullback-Leibler divergence to the target distribution. The parameters in M-PMC are updated using a single step of expectation maximization (EM), which limits its accuracy. In this work, we introduce a novel M-PMC algorithm that optimizes the parameters of a mixture proposal distribution, where parameter updates are resolved via stochastic optimization instead of EM. The stochastic gradients w.r.t. each of the mixture parameters are approximated using a population of Markov chain Monte Carlo samplers. We validate the proposed scheme via numerical simulations on an example where the considered target distribution is multimodal.
AB - The population Monte Carlo (PMC) algorithm is a popular adaptive importance sampling (AIS) method used for approximate computation of intractable integrals. Over the years, many advances have been made in the theory and implementation of PMC schemes. The mixture PMC (M-PMC) algorithm, for instance, optimizes the parameters of a mixture proposal distribution in a way that minimizes that Kullback-Leibler divergence to the target distribution. The parameters in M-PMC are updated using a single step of expectation maximization (EM), which limits its accuracy. In this work, we introduce a novel M-PMC algorithm that optimizes the parameters of a mixture proposal distribution, where parameter updates are resolved via stochastic optimization instead of EM. The stochastic gradients w.r.t. each of the mixture parameters are approximated using a population of Markov chain Monte Carlo samplers. We validate the proposed scheme via numerical simulations on an example where the considered target distribution is multimodal.
KW - Bayesian inference
KW - MCMC sampling
KW - population Monte Carlo
KW - Rényi divergence
KW - stochastic optimization
UR - https://www.scopus.com/pages/publications/85089230923
U2 - 10.1109/ICASSP40776.2020.9053410
DO - 10.1109/ICASSP40776.2020.9053410
M3 - Conference contribution
AN - SCOPUS:85089230923
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 5475
EP - 5479
BT - 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020
Y2 - 4 May 2020 through 8 May 2020
ER -