Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks
This work addresses a key bottleneck in computational science for researchers needing efficient and accurate sampling of complex distributions, though it is incremental as it builds on existing autoregressive and Monte Carlo methods.
The authors tackled the problem of bias and high variance in sampling high-dimensional probability distributions using autoregressive neural networks with Markov chain Monte Carlo, proposing a method that makes the approximation unbiased and low-variance by leveraging physical symmetries and variable-size cluster updates. They demonstrated its viability for first- and second-order phase transitions in classical spin systems, including critical systems and metastable states.
Efficient sampling of complex high-dimensional probability distributions is a central task in computational science. Machine learning methods like autoregressive neural networks, used with Markov chain Monte Carlo sampling, provide good approximations to such distributions, but suffer from either intrinsic bias or high variance. In this Letter, we propose a way to make this approximation unbiased and with low variance. Our method uses physical symmetries and variable-size cluster updates which utilize the structure of autoregressive factorization. We test our method for first- and second-order phase transitions of classical spin systems, showing its viability for critical systems and in the presence of metastable states.