Adaptive Online Experimental Design for Causal Discovery (2405.11548v3)

Abstract: Causal discovery aims to uncover cause-and-effect relationships encoded in causal graphs by leveraging observational, interventional data, or their combination. The majority of existing causal discovery methods are developed assuming infinite interventional data. We focus on data interventional efficiency and formalize causal discovery from the perspective of online learning, inspired by pure exploration in bandit problems. A graph separating system, consisting of interventions that cut every edge of the graph at least once, is sufficient for learning causal graphs when infinite interventional data is available, even in the worst case. We propose a track-and-stop causal discovery algorithm that adaptively selects interventions from the graph separating system via allocation matching and learns the causal graph based on sampling history. Given any desired confidence value, the algorithm determines a termination condition and runs until it is met. We analyze the algorithm to establish a problem-dependent upper bound on the expected number of required interventional samples. Our proposed algorithm outperforms existing methods in simulations across various randomly generated causal graphs. It achieves higher accuracy, measured by the structural hamming distance (SHD) between the learned causal graph and the ground truth, with significantly fewer samples.

• The paper presents a novel track-and-stop algorithm that adaptively selects interventions to efficiently recover causal graphs using limited data.
• It establishes a graph separating system within a fixed confidence framework, significantly reducing the number of required interventional samples.
• Extensive simulations demonstrate that the algorithm outperforms traditional methods, offering practical benefits in fields with costly or constrained data collection.

Adaptive Online Experimental Design for Causal Discovery

This paper presents an innovative approach to causal discovery, focusing on data interventional efficiency within an online learning framework. Specifically, it targets the inefficiencies of current methods that assume infinite interventional data for causal graph learning. By drawing inspiration from pure exploration strategies in multi-armed bandit problems, the authors propose a novel track-and-stop algorithm designed to adaptively select interventions based on the history of sampling, ultimately aiming to reveal the causal graph with precision.

The authors form a theoretical basis by establishing a graph separating system, which is a set of interventions that ensure each edge of the causal graph is "cut" at least once, facilitating the learning of causal graphs even with limited data. This system, traditionally requiring infinite data for robustness, is adapted here for scenarios with finite interventional data.

Key features of the proposed algorithm encompass the following:

1. Adaptive Intervention Selection: The track-and-stop approach adaptively selects interventions from the graph separating system, optimizing each decision based on prior sampling outcomes. This is contrasted with traditional methods that predefine intervention sequences or require exhaustive intervention data.
2. Fixed Confidence Framework: The algorithm is designed to operate within a fixed confidence setting. It endeavors to identify the true directed acyclic graph (DAG) within a pre-specified confidence level, minimizing the number of required interventions significantly.
3. Problem-Dependent Sample Efficiency: An analytical examination of the algorithm provides a problem-dependent upper bound on the expected number of required interventional samples, setting it apart as a particularly data-efficient method within the causal discovery domain.
4. Algorithmic Soundness and Asymptotic Optimality: The algorithm is shown to achieve asymptotic optimal performance, aligning expected intervention requirements with theoretical lower bounds on data sufficiency, as confirmed through extensive simulation experiments.

The paper demonstrates the empirical effectiveness of the algorithm using simulated data, including complete and Erdös-Rényi random graphs, as well as real-world data exemplified in the SACHS Bayesian network. Across these experiments, the track-and-stop algorithm consistently outperformed existing causal discovery approaches such as random intervention plans, DCT-based methods, and the GIES algorithm, achieving higher accuracy with fewer samples.

In practical terms, this research carries substantial implications. The ability to efficiently uncover causal structures with a minimized number of interventional samples is particularly advantageous in fields where data collection is costly or ethically constrained, like healthcare and social sciences. Theoretically, the work lays groundwork for further exploration into adaptive online experimental designs, providing a robust foundation for more refined causal inference models that can dynamically adjust to limited datasets.

Future developments in adaptive causal discovery could entail enhancements in computational efficiency and robustness, particularly under complex real-world conditions with noisy observational or interventional data. Additionally, integrating this framework with deep learning models could potentially open new avenues in handling high-dimensional datasets where traditional methods might falter.

In conclusion, this paper provides a significant step forward in causal discovery, fostering a deeper understanding of adaptive algorithmic strategies within the constraints of finite data, thereby expanding the practical applicability and scope of causal inference methodologies.