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We introduce a quantitative framework for separating skill and chance in games by modeling them as complementary sources of control over stochastic decision trees. We define the Skill-Luck Index S(G) in [-1, 1] by decomposing game outcomes…
Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC)…
This work presents a new sufficient condition for synthesizing nonlinear controllers that yield bounded closed-loop tracking error transients despite the presence of unmatched uncertainties that are concurrently being learned online. The…
Although machine learning (ML)-based performance outcome prediction is an important topic in contemporary sports science, one important issue is the limited understanding of the cross-individual generalizability of ML models in sports…
Ranking items based on pairwise comparisons is common, from using match outcomes to rank sports teams to using purchase or survey data to rank consumer products. Statistical inference-based methods such as the Bradley-Terry model, which…
In inference problems involving a multi-dimensional parameter $\theta$, it is often natural to consider decision rules that have a risk which is invariant under some group $G$ of permutations of $\theta$. We show that this implies that the…
Trajectory planning involving multi-agent interactions has been a long-standing challenge in the field of robotics, primarily burdened by the inherent yet intricate interactions among agents. While game-theoretic methods are widely…
Intransitivity is supposed to be a main reason for deficits in coevolutionary progress and inheritable superiority. Besides, coevolutionary dynamics is characterized by interactions yielding subjective fitness, but aiming at solutions that…
Forecasting players in sports has grown in popularity due to the potential for a tactical advantage and the applicability of such research to multi-agent interaction systems. Team sports contain a significant social component that…
Ranking problems based on pairwise comparisons, such as those arising in online gaming, often involve a large pool of items to order. In these situations, the gap in performance between any two items can be significant, and the smallest and…
Bradley-Terry-Luce (BTL) model estimation is a well-established strategy to rank a collection of items given a dataset of pairwise comparisons. Although the theoretical performance of BTL estimation methods, such as spectral and maximum…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
It was recently observed that Elo ratings fail at preserving transitive relations among strategies and therefore cannot correctly extract the transitive component of a game. We provide a characterization of transitive games as a weak…
We consider the problem of estimating `preference' or `strength' parameters in three-way comparison experiments, each composed of a series of paired comparisons, but where only the single `preferred' or `strongest' candidate is known in…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
This paper develops metrics from a social network perspective that are directly translatable to the outcome of a basketball game. We extend a state-of-the-art multi-resolution stochastic process approach to modeling basketball by modeling…
Evaluating the pedagogical quality of AI tutors remains challenging: standard NLG metrics do not determine whether responses identify mistakes, scaffold reasoning, or avoid revealing the answers. For the task of mistake remediation, we…
This study explores the relationship between the performance of a football team and the topological parameters of temporal passing networks. To achieve this, we propose a method to identify moments of high and low team performance based on…
In-game win probability models, which provide a sports team's likelihood of winning at each point in a game based on historical observations, are becoming increasingly popular. In baseball, basketball and American football, they have become…
Feature and trait allocation models are fundamental objects in Bayesian nonparametrics and play a prominent role in several applications. Existing approaches, however, typically assume full exchangeability of the data, which may be…