  Understanding the principles of real-world biological multi-agent behaviors
is a current challenge in various scientific and engineering fields. The rules
regarding the real-world biological multi-agent behaviors such as team sports
are often largely unknown due to their inherently higher-order interactions,
cognition, and body dynamics. Estimation of the rules from data, i.e.,
data-driven approaches such as machine learning, provides an effective way for
the analysis of such behaviors. Although most data-driven models have
non-linear structures and high prediction performances, it is sometimes hard to
interpret them. This survey focuses on data-driven analysis for quantitative
understanding of invasion team sports behaviors such as basketball and
football, and introduces two main approaches for understanding such multi-agent
behaviors: (1) extracting easily interpretable features or rules from data and
(2) generating and controlling behaviors in visually-understandable ways. The
first approach involves the visualization of learned representations and the
extraction of mathematical structures behind the behaviors. The second approach
can be used to test hypotheses by simulating and controlling future and
counterfactual behaviors. Lastly, the potential practical applications of
extracted rules, features, and generated behaviors are discussed. These
approaches can contribute to a better understanding of multi-agent behaviors in
the real world.
