Toward Universal Laws of Outlier Propagation

We argue that Algorithmic Information Theory (AIT) admits a principled way to quantify outliers in terms of so-called randomness deficiency. For the probability distribution generated by a causal Bayesian network, we show that the randomness deficiency of the joint state decomposes into randomness deficiencies of each causal mechanism, subject to the Independence of Mechanisms Principle. Accordingly, anomalous joint observations can be quantitatively attributed to their root causes, i.e., the mechanisms that behaved anomalously. As an extension of Levin's law of randomness conservation, we show that weak outliers cannot cause strong ones when Independence of Mechanisms holds. We show how these information theoretic laws provide a better understanding of the behaviour of outliers defined with respect to existing scores.

An Elo-like System for Massive Multiplayer Competitions

Rating systems play an important role in competitive sports and games. They provide a measure of player skill, which incentivizes competitive performances and enables balanced match-ups. In this paper, we present a novel Bayesian rating system for contests with many participants. It is widely applicable to competition formats with discrete ranked matches, such as online programming competitions, obstacle courses races, and some video games. The simplicity of our system allows us to prove theoretical bounds on robustness and runtime. In addition, we show that the system aligns incentives: that is, a player who seeks to maximize their rating will never want to underperform. Experimentally, the rating system rivals or surpasses existing systems in prediction accuracy, and computes faster than existing systems by up to an order of magnitude.