General Causal Imputation via Synthetic Interventions (2410.20647v1)

Abstract: Given two sets of elements (such as cell types and drug compounds), researchers typically only have access to a limited subset of their interactions. The task of causal imputation involves using this subset to predict unobserved interactions. Squires et al. (2022) have proposed two estimators for this task based on the synthetic interventions (SI) estimator: SI-A (for actions) and SI-C (for contexts). We extend their work and introduce a novel causal imputation estimator, generalized synthetic interventions (GSI). We prove the identifiability of this estimator for data generated from a more complex latent factor model. On synthetic and real data we show empirically that it recovers or outperforms their estimators.

• The paper introduces the GSI estimator, extending SI models to enable accurate causal imputation in multi-dimensional data.
• The authors provide rigorous theoretical analysis, proving the identifiability and robustness of GSI under relaxed latent factor assumptions.
• Empirical evaluations on synthetic and real datasets, including CMAP, demonstrate GSI’s superior performance in recovering unobserved interactions.

General Causal Imputation via Synthetic Interventions

This paper advances the discourse on causal imputation, a critical task in the intersection of causal inference and machine learning. The authors extend the existing methods for estimating unobserved interactions between two sets of elements using causal structures. Through their work, they present a novel estimator dubbed Generalized Synthetic Interventions (GSI). The paper builds substantially on prior work, specifically the synthetic interventions (SI) estimator, to effectively tackle causal imputation challenges.

Key Contributions

The primary contributions of the paper are threefold:

1. Introduction of GSI: A novel causal imputation estimator is formulated. The GSI estimator extends the existing SI-I (Action) and SI-C (Context) models to accommodate multi-dimensional outputs more effectively. This extension is theoretically grounded, proving the identifiability of the GSI when data is generated under a more complex latent factor model. The authors argue that this model is better suited for data with inherent high-dimensional complexity.
2. Theoretical Analysis: The paper rigorously develops the theoretical underpinnings that guarantee the identifiability of the GSI estimator. By relaxing and adjusting assumptions related to latent factor models, the authors demonstrate that the GSI maintains the desired statistical properties required for successful imputation.
3. Empirical Evaluation: Comprehensive evaluations are conducted on both synthetic and real datasets. The experiments indicate that GSI offers superior performance in recovering unobserved interactions compared to existing estimators. In particular, the paper examines the well-documented CMAP dataset, providing compelling empirical evidence for the effectiveness of their approach.

Methodological Insights

The paper posits the extension of the latent factor models applied in the causal imputation domain. Unlike previous approaches, the GSI incorporates flexibility by allowing different latent factors for different dimensions in the evaluated outcome tensor. This accommodates a broader range of interaction types and potential correlations within high-dimensional data fields, such as gene expression levels.

Key steps involve breaking the previous assumption symmetry between actions (compounds) and contexts (cell types) in the tensor analysis, enabling a more granular and accurate predictive model. This refinement allows the GSI to apply linear regression independently across dimensions, thus acknowledging and modeling the possible heterogeneity across dimensions more effectively.

Implications and Future Directions

The implications of this research are noteworthy for both theoretical advances and practical applications. The more generalized model proposed by the authors can be adapted easily to other high-dimensional datasets where interaction effects need to be inferred, such as pharmaceutical drug testing and multi-omics studies in biological sciences.

Future research as suggested by the authors could explore nonlinear extensions of this estimation framework to capture interaction complexities beyond linear relationships. Additionally, application to more diverse datasets could further validate the robustness and general applicability of GSI, possibly exploring computational efficiencies to address scalability issues.

In terms of practical implications, the real-world applicability of GSI to datasets like CMAP points to its potential as a reliable tool in bioinformatics and related fields where causality and interaction effects are of paramount importance.

Conclusion

Overall, this paper makes a significant technical contribution to the field of causal imputation by proposing the GSI estimator. The advancements in handling multi-dimensional data interactions extend the boundaries of what can be achieved in data scenarios characterized by complexity and partial observability. Moreover, the introduction of GSI provides a crucial contribution to the interpretation of high-dimensional data where previous methodologies may have fallen short.