# Detecting and Identifying Selection Structure in Sequential Data

arXiv: https://arxiv.org/abs/2407.00529 · HTML: https://mlsanity.com/paper/2407.00529/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 31 references that are in the map.
- First posted on arXiv 29 Jun 2024.

## Builds on (most cited first, 5 of 5)

- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Causal Calculus in the Presence of Cycles, Latent Confounders and Selection Bias](https://mlsanity.com/paper/1901.00433/) (2019)
- [Local Constraint-Based Causal Discovery under Selection Bias](https://mlsanity.com/paper/2203.01848/) (2022)
- [Foundations of Structural Causal Models with Latent Selection](https://mlsanity.com/paper/2401.06925/) (2024)

## Built on by (most cited first, 9 of 9)

- [When Selection Meets Intervention: Additional Complexities in Causal Discovery](https://mlsanity.com/paper/2503.07302/) (2025)
- [Latent Variable Causal Discovery under Selection Bias](https://mlsanity.com/paper/2512.11219/) (2025)
- [Identifying Selections for Unsupervised Subtask Discovery](https://mlsanity.com/paper/2410.21616/) (2024)
- [Nonparametric Identification of Latent Concepts](https://mlsanity.com/paper/2510.00136/) (2025)
- [Selection, Reflection and Self-Refinement: Revisit Reasoning Tasks via a Causal Lens](https://mlsanity.com/paper/2510.08222/) (2025)
- [Beyond the Black Box: Identifiable Interpretation and Control in Generative Models via Causal Minimality](https://mlsanity.com/paper/2512.10720/) (2025)
- [Towards a holistic understanding of Selection Bias for Causal Effect Identification](https://mlsanity.com/paper/2605.13430/) (2026)
- [Causal Modeling of Selection in Evolution](https://mlsanity.com/paper/2606.05689/) (2026)
- [Identifying Structural Biases from Causal Mechanism Shifts](https://mlsanity.com/paper/2606.18834/) (2026)

## Abstract (arXiv)

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.