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This paper introduces a novel reachability problem for the scenario involving two agents, where one agent follows another agent using a feedback strategy. The geometry of the reachable set for an agent, termed \emph{dependent reachable…
Despite the widespread use of Uniform Manifold Approximation and Projection (UMAP), the impact of its stochastic optimization process on the results remains underexplored. We observed that it often produces unstable results where the…
Solutions to pursuit-evasion and surveillance-evasion differential games are typically computed and expressed using open-loop representations, with the synthesis of feedback strategies significantly less common. We propose a numerical…
Technological advances have paved the way for collecting high-resolution network data in basketball, football, and other team-based sports. Such data consist of interactions among players of competing teams indexed by space and time.…
This study proposes a statistically grounded framework for real-time win probability evaluation and player assessment in score-based team sports, based on minute-by-minute cumulative box-score data. We introduce a continuous dominance…
During the 2017 NBA playoffs, Celtics coach Brad Stevens was faced with a difficult decision when defending against the Cavaliers: "Do you double and risk giving up easy shots, or stay at home and do the best you can?" It's a tough call,…
Sophisticated trajectory prediction models that effectively mimic team dynamics have many potential uses for sports coaches, broadcasters and spectators. However, through experiments on soccer data we found that it can be surprisingly…
Daily fantasy sports (DFS) are weekly or daily online contests where real-game performances of individual players are converted to fantasy points (FPTS). Users select players for their lineup to maximize their FPTS within a set player…
This paper presents a new framework for player valuation in European football, by fusing principles from financial mathematics and network theory. The valuation model leverages a "passing matrix" to encapsulate player interactions on the…
Analysis of invasive sports such as soccer is challenging because the game situation changes continuously in time and space, and multiple agents individually recognize the game situation and make decisions. Previous studies using deep…
This paper proposes and studies a class of discrete-time finite-time-horizon Stackelberg mean-field games, with one leader and an infinite number of identical and indistinguishable followers. In this game, the objective of the leader is to…
We consider a variant of the target defense problem where a single defender is tasked to capture a sequence of incoming intruders. Both the defender and the intruders have non-holonomic dynamics. The intruders' objective is to breach the…
This paper studies a variant of the multi-player reach-avoid game played between intruders and defenders with applications to perimeter defense. The intruder team tries to score by sending as many intruders as possible to the target area,…
Conditional density estimation (CDE) is a fundamental task in machine learning that aims to model the full conditional law $\mathbb{P}(\mathbf{y} \mid \mathbf{x})$, beyond mere point prediction (e.g., mean, mode). A core challenge is…
Assessing the spatial fairness of predictive models involves establishing whether they are statistically penalizing (favoring) individuals associated with certain geographical locations. Literature on this topic makes the fundamental…
We introduce deceptive signaling framework as a new defense measure against advanced adversaries in cyber-physical systems. In general, adversaries look for system-related information, e.g., the underlying state of the system, in order to…
The global sports analytics industry has a market value of USD 3.78 billion in 2023. The increase of wearables such as GPS sensors has provided analysts with large fine-grained datasets detailing player performance. Traditional analysis of…
Current football imitation research primarily aims to opti mize reward-based objectives, such as goals scored or win rate proxies, paying less attention to accurately replicat ing real-world team tactical behaviors. We introduce Tac SIm, a…
In soccer, passing is the most frequent interaction between players and plays a significant role in creating scoring chances. Experts are interested in analyzing players' passing behavior to learn passing tactics, i.e., how players build up…
We develop a general framework for reasoning about distances between transition systems with quantitative information. Taking as starting point an arbitrary distance on system traces, we show how this leads to natural definitions of a…