Efficient Local Causal Discovery for Estimating Causal Effects

Core Concepts

Local causal discovery algorithms can efficiently identify the set of possible average treatment effects by leveraging the local structure around the treatment node, without requiring the full causal graph.

Abstract

The paper introduces a new local causal discovery algorithm called Local Discovery using Eager Collider Checks (LDECC) that orients the parents of the treatment node differently from existing methods. LDECC leverages unshielded colliders to efficiently identify the set of possible average treatment effects, without requiring the full causal graph structure. The key highlights and insights are: LDECC runs conditional independence tests in a different order than existing local discovery algorithms, and uses an "eager collider check" to orient the parents of the treatment node. LDECC is shown to have complementary strengths to existing local discovery algorithms like Sequential Discovery (SD) in terms of computational requirements. There are classes of graphs where LDECC exponentially outperforms SD, and vice versa. LDECC and SD rely on different faithfulness assumptions. The paper proposes a procedure that combines the two algorithms to identify the set of possible average treatment effects under strictly weaker assumptions than either algorithm alone. Empirical results on synthetic and semi-synthetic data show that LDECC performs comparably to existing methods while typically running fewer conditional independence tests.

Stats

The number of nodes in the graph is denoted as |V|. The maximum size of the Markov blanket of the treatment node X is denoted as D = maxV∈MB+(X) |Ne(V)|. The maximum size of the separating set for unshielded colliders that can orient the parents of X is denoted as S = maxP∈Pa(X) minα∈POC(P) sep(α). The maximum size of the separating set for the closest unshielded collider that can orient a parent of X is denoted as C = maxP∈Pa(X) sep(CUC(P)). The maximum size of the neighborhoods of nodes on the path to the closest unshielded collider that can orient a parent of X is denoted as E = max{V:π(V)<π(CUC(P))} |Ne(V)|.

Quotes

"Fortunately, only the local graph structure around the treatment is required to identify the set of possible ATE values, a fact exploited by local discovery algorithms to improve computational efficiency." "LDECC can orient the smallest subset of X's neighbors that d-separate it from {A, B} as parents." "There exist classes of graphs where LDECC exponentially outperforms existing local discovery algorithms and vice versa."

Key Insights Distilled From

Local Causal Discovery for Estimating Causal Effects

by Shantanu Gup... at arxiv.org 04-11-2024

https://arxiv.org/pdf/2302.08070.pdf

Deeper Inquiries

How can the faithfulness assumptions required by LDECC and SD be further weakened to identify the set of possible average treatment effects

In the context of local causal discovery, the faithfulness assumptions required by LDECC and SD can be further weakened to identify the set of possible average treatment effects by considering additional conditions and constraints. One approach is to incorporate more nuanced criteria for detecting faithfulness violations and adjusting the algorithms accordingly. For example, in LDECC, the Eager Collider Checks (ECC) can be refined to account for specific patterns of conditional independence that may indicate the presence of unfaithful structures in the causal graph. By fine-tuning the ECC criteria based on the characteristics of the data and the graph, LDECC can adapt to a wider range of faithfulness violations and still identify the correct set of possible average treatment effects. Similarly, in SD, the Sequential Discovery algorithm can be enhanced by introducing additional checks or tests that target specific types of faithfulness violations. By expanding the criteria for local structure learning and orientation, SD can improve its ability to identify the set of possible average treatment effects under weaker faithfulness assumptions. This may involve incorporating information from neighboring nodes, exploring alternative paths in the graph, or considering different configurations of conditional independence relationships. By iteratively refining the faithfulness assumptions and incorporating more sophisticated techniques for detecting violations and adjusting the algorithms, both LDECC and SD can be further optimized to identify the set of possible average treatment effects with greater accuracy and efficiency.

What other types of local information, beyond unshielded colliders, could be leveraged to improve the efficiency of causal discovery for estimating causal effects

Beyond unshielded colliders, other types of local information that could be leveraged to improve the efficiency of causal discovery for estimating causal effects include the identification of Markov blankets, the exploration of parent-child relationships, and the detection of minimal neighbor separators. By focusing on these aspects of the causal graph, algorithms like LDECC and SD can gain deeper insights into the local structure surrounding the treatment node and its impact on the outcome variable. Markov Blankets: By identifying the Markov blankets of relevant nodes, algorithms can uncover the direct dependencies and influences that contribute to the causal relationships in the graph. This information can help in orienting edges and determining the set of possible average treatment effects more accurately. Parent-Child Relationships: Understanding the parent-child relationships in the local structure can provide valuable insights into the causal mechanisms at play. By prioritizing the orientation of edges based on these relationships, algorithms can streamline the causal discovery process and improve efficiency. Minimal Neighbor Separators: Detecting minimal neighbor separators can help in identifying the minimal sets of nodes that need to be adjusted for in order to estimate causal effects accurately. By leveraging this information, algorithms can focus on the most relevant variables and streamline the estimation process. By incorporating these additional types of local information into the causal discovery algorithms, researchers can enhance the efficiency and effectiveness of estimating causal effects from observational data.

How can the insights from this work on local causal discovery be extended to settings with hidden confounders or multiple treatments

The insights from this work on local causal discovery can be extended to settings with hidden confounders or multiple treatments by adapting the algorithms to account for these complexities in the causal graph. Here are some ways in which the insights can be applied: Hidden Confounders: In the presence of hidden confounders, algorithms like LDECC and SD can be modified to incorporate latent variables into the causal graph and adjust for their effects on the observed variables. By considering the potential influence of hidden confounders on the causal relationships, the algorithms can provide more accurate estimates of causal effects and account for unobserved factors that may impact the outcomes. Multiple Treatments: When dealing with multiple treatments, the algorithms can be extended to handle the interactions and dependencies between different interventions. By analyzing the local structure around each treatment node and considering the combined effects of multiple treatments, the algorithms can estimate the causal effects of each treatment on the outcome variable while accounting for the potential interactions between them. By adapting the algorithms to address hidden confounders and multiple treatments, researchers can apply the insights from local causal discovery to more complex causal inference scenarios and improve the accuracy and robustness of estimating causal effects in diverse settings.