  We argue that the selective inclusion of data points based on latent
objectives is common in practical situations, such as music sequences. Since
this selection process often distorts statistical analysis, previous work
primarily views it as a bias to be corrected and proposes various methods to
mitigate its effect. However, while controlling this bias is crucial, selection
also offers an opportunity to provide a deeper insight into the hidden
generation process, as it is a fundamental mechanism underlying what we
observe. In particular, overlooking selection in sequential data can lead to an
incomplete or overcomplicated inductive bias in modeling, such as assuming a
universal autoregressive structure for all dependencies. Therefore, rather than
merely viewing it as a bias, we explore the causal structure of selection in
sequential data to delve deeper into the complete causal process. Specifically,
we show that selection structure is identifiable without any parametric
assumptions or interventional experiments. Moreover, even in cases where
selection variables coexist with latent confounders, we still establish the
nonparametric identifiability under appropriate structural conditions.
Meanwhile, we also propose a provably correct algorithm to detect and identify
selection structures as well as other types of dependencies. The framework has
been validated empirically on both synthetic data and real-world music.
