# COKE: Causal Discovery with Chronological Order and Expert Knowledge in High Proportion of Missing Manufacturing Data

arXiv: https://arxiv.org/abs/2407.12254 · HTML: https://mlsanity.com/paper/2407.12254/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 17 Jul 2024.

## Builds on (most cited first, 9 of 9)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Ordering-Based Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/2105.06631/) (2021)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [A fast PC algorithm for high dimensional causal discovery with multi-core PCs](https://mlsanity.com/paper/1502.02454/) (2015)
- [Causal Discovery from Incomplete Data: A Deep Learning Approach](https://mlsanity.com/paper/2001.05343/) (2020)
- [MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models](https://mlsanity.com/paper/2205.13869/) (2022)
- [Causal Discovery for Manufacturing Domains](https://mlsanity.com/paper/1605.04056/) (2016)
- [Identification of Causal Structure in the Presence of Missing Data with Additive Noise Model](https://mlsanity.com/paper/2312.12206/) (2023)

## Built on by (most cited first, 5 of 5)

- [A Survey of Reasoning and Agentic Systems in Time Series with Large Language Models](https://mlsanity.com/paper/2509.11575/) (2025)
- [Time-IMM: A Dataset and Benchmark for Irregular Multimodal Multivariate Time Series](https://mlsanity.com/paper/2506.10412/) (2025)
- [PromptTSS: A Prompting-Based Approach for Interactive Multi-Granularity Time Series Segmentation](https://mlsanity.com/paper/2506.11170/) (2025)
- [Perseus: Interactive Time Series Segmentation with Sparse Supervision via Stateful Memory](https://mlsanity.com/paper/2510.09930/) (2025)
- [Causal Preference Elicitation](https://mlsanity.com/paper/2602.01483/) (2026)

## Abstract (arXiv)

Understanding causal relationships between machines is crucial for fault diagnosis and optimization in manufacturing processes. Real-world datasets frequently exhibit up to 90% missing data and high dimensionality from hundreds of sensors. These datasets also include domain-specific expert knowledge and chronological order information, reflecting the recording order across different machines, which is pivotal for discerning causal relationships within the manufacturing data. However, previous methods for handling missing data in scenarios akin to real-world conditions have not been able to effectively utilize expert knowledge. Conversely, prior methods that can incorporate expert knowledge struggle with datasets that exhibit missing values. Therefore, we propose COKE to construct causal graphs in manufacturing datasets by leveraging expert knowledge and chronological order among sensors without imputing missing data. Utilizing the characteristics of the recipe, we maximize the use of samples with missing values, derive embeddings from intersections with an initial graph that incorporates expert knowledge and chronological order, and create a sensor ordering graph. The graph-generating process has been optimized by an actor-critic architecture to obtain a final graph that has a maximum reward. Experimental evaluations in diverse settings of sensor quantities and missing proportions demonstrate that our approach compared with the benchmark methods shows an average improvement of 39.9% in the F1-score. Moreover, the F1-score improvement can reach 62.6% when considering the configuration similar to real-world datasets, and 85.0% in real-world semiconductor datasets. The source code is available at https://github.com/OuTingYun/COKE.