Empirical evaluation of normalizing flows in Markov Chain Monte Carlo

Recent advances in MCMC use normalizing flows to precondition target distributions and enable jumps to distant regions. However, there is currently no systematic comparison of different normalizing flow architectures for MCMC. As such, many works choose simple flow architectures that are readily available and do not consider other models. Guidelines for choosing an appropriate architecture would reduce analysis time for practitioners and motivate researchers to take the recommended models as foundations to be improved. We provide the first such guideline by extensively evaluating many normalizing flow architectures on various flow-based MCMC methods and target distributions. When the target density gradient is available, we show that flow-based MCMC outperforms classic MCMC for suitable NF architecture choices with minor hyperparameter tuning. When the gradient is unavailable, flow-based MCMC wins with off-the-shelf architectures. We find contractive residual flows to be the best general-purpose models with relatively low sensitivity to hyperparameter choice. We also provide various insights into normalizing flow behavior within MCMC when varying their hyperparameters, properties of target distributions, and the overall computational budget.

Control, Transport and Sampling: Towards Better Loss Design

Leveraging connections between diffusion-based sampling, optimal transport, and optimal stochastic control through their shared links to the Schr\"odinger bridge problem, we propose novel objective functions that can be used to transport $\nu$ to $\mu$, consequently sample from the target $\mu$, via optimally controlled dynamics. We highlight the importance of the pathwise perspective and the role various optimality conditions on the path measure can play for the design of valid training losses, the careful choice of which offer numerical advantages in practical implementation.

Predicting the Popularity of Games on Steam

The video game industry has seen rapid growth over the last decade. Thousands of video games are released and played by millions of people every year, creating a large community of players. Steam is a leading gaming platform and social networking site, which allows its users to purchase and store games. A by-product of Steam is a large database of information about games, players, and gaming behavior. In this paper, we take recent video games released on Steam and aim to discover the relation between game popularity and a game's features that can be acquired through Steam. We approach this task by predicting the popularity of Steam games in the early stages after their release and we use a Bayesian approach to understand the influence of a game's price, size, supported languages, release date, and genres on its player count. We implement several models and discover that a genre-based hierarchical approach achieves the best performance. We further analyze the model and interpret its coefficients, which indicate that games released at the beginning of the month and games of certain genres correlate with game popularity.