On Discovery of Local Independence over Continuous Variables via Neural Contextual Decomposition

TL;DR

This paper introduces CSSI, a new form of local independence for continuous variables, and proposes NCD, a neural method to discover these relationships in complex systems.

Contribution

It defines CSSI, characterizes its properties, and develops NCD to identify local independence relationships in continuous variable systems.

Findings

Successfully discovers ground truth CSSI in synthetic data

Demonstrates effectiveness on complex physical systems

Provides a theoretical foundation for CSSI properties

Abstract

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.