Sampling from a Neural Network

In this article, the video game Dota 2 is used as an illustration of video games where two teams have to confront. This is a very popular game where billions of matches are available for enhancing statistical analysis and fostering further method developments. Here, we focus on sampling teams or pairs of teams favouring more imbalanced matches, based upon the scores observed either for one team or for a couple of teams. An artificial neural network models the expected outcome which is then used to sample teams through a Metropolis-Hastings algorithm. The main result is establishing the polynomial convergence speed bound for both cases, that is sampling random teams and sampling random pairs of teams. An empirical experiment is also provided when sampling pairs of teams for Dota after learning matches outcomes from a database of 2 million matches, showing that the convergence may happen much more quickly.