On Discovery of Local Independence over Continuous Variables via Neural Contextual Decomposition
<|reference_start|>On Discovery of Local Independence over Continuous Variables via Neural Contextual Decomposition: Conditional independence provides a way to understand causal relationships among the variables of interest. An underlying system may exhibit more fine-grained causal relationships especially between a variable and its parents, which will be called the local independence relationships. One of the most widely studied local relationships is Context-Specific Independence (CSI), which holds in a specific assignment of conditioned variables. However, its applicability is often limited since it does not allow continuous variables: data conditioned to the specific value of a continuous variable contains few instances, if not none, making it infeasible to test independence. In this work, we define and characterize the local independence relationship that holds in a specific set of joint assignments of parental variables, which we call context-set specific independence (CSSI). We then provide a canonical representation of CSSI and prove its fundamental properties. Based on our theoretical findings, we cast the problem of discovering multiple CSSI relationships in a system as finding a partition of the joint outcome space. Finally, we propose a novel method, coined neural contextual decomposition (NCD), which learns such partition by imposing each set to induce CSSI via modeling a conditional distribution. We empirically demonstrate that the proposed method successfully discovers the ground truth local independence relationships in both synthetic dataset and complex system reflecting the real-world physical dynamics.<|reference_end|>
@article{hwang2024on,
    title={On Discovery of Local Independence over Continuous Variables via Neural
  Contextual Decomposition},
    author={Inwoo Hwang, Yunhyeok Kwak, Yeon-Ji Song, Byoung-Tak Zhang, Sanghack
  Lee},
    journal={arXiv preprint arXiv:2405.07220},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.07220},
    primaryClass={cs.LG cs.AI stat.ML}
}