Learning to Sample Better
This is an incremental advance for researchers in computational statistics and machine learning, focusing on domain-specific applications in sampling methods.
The paper tackles the problem of improving Monte-Carlo sampling techniques by using generative models based on dynamical transportation of measures, showing how learned maps can enhance sampling in a feedback loop.
These lecture notes provide an introduction to recent advances in generative modeling methods based on the dynamical transportation of measures, by means of which samples from a simple base measure are mapped to samples from a target measure of interest. Special emphasis is put on the applications of these methods to Monte-Carlo (MC) sampling techniques, such as importance sampling and Markov Chain Monte-Carlo (MCMC) schemes. In this context, it is shown how the maps can be learned variationally using data generated by MC sampling, and how they can in turn be used to improve such sampling in a positive feedback loop.