Automatic Differentiable Monte Carlo: Theory

Differentiable programming emerges as the new programming paradigm empowering the rapid development of deep learning as it has been shown equally powerful in computational physics. Here we propose a general theory framework with detach function techniques enabling infinite order automatic differentiation on Monte Carlo expectations with unnormalized probability distributions. By introducing automatic differentiable Monte Carlo (ADMC), we can leverage state-of-the-art machine learning framework and toolbox to traditional Monte Carlo approaches in statistics and physics by simply implementing relevant Monte Carlo algorithms on computation graphs.