Adjacency-Faithfulness and Conservative Causal Inference (1206.6843v1)

Abstract: Most causal inference algorithms in the literature (e.g., Pearl (2000), Spirtes et al. (2000), Heckerman et al. (1999)) exploit an assumption usually referred to as the causal Faithfulness or Stability condition. In this paper, we highlight two components of the condition used in constraint-based algorithms, which we call "Adjacency-Faithfulness" and "Orientation-Faithfulness". We point out that assuming Adjacency-Faithfulness is true, it is in principle possible to test the validity of Orientation-Faithfulness. Based on this observation, we explore the consequence of making only the Adjacency-Faithfulness assumption. We show that the familiar PC algorithm has to be modified to be (asymptotically) correct under the weaker, Adjacency-Faithfulness assumption. Roughly the modified algorithm, called Conservative PC (CPC), checks whether Orientation-Faithfulness holds in the orientation phase, and if not, avoids drawing certain causal conclusions the PC algorithm would draw. However, if the stronger, standard causal Faithfulness condition actually obtains, the CPC algorithm is shown to output the same pattern as the PC algorithm does in the large sample limit. We also present a simulation study showing that the CPC algorithm runs almost as fast as the PC algorithm, and outputs significantly fewer false causal arrowheads than the PC algorithm does on realistic sample sizes. We end our paper by discussing how score-based algorithms such as GES perform when the Adjacency-Faithfulness but not the standard causal Faithfulness condition holds, and how to extend our work to the FCI algorithm, which allows for the possibility of latent variables.

• The paper demonstrates that relaxing full Causal Faithfulness to only Adjacency-Faithfulness yields valid causal inferences, reducing erroneous orientations.
• It introduces the Conservative PC algorithm, which efficiently tests Orientation-Faithfulness and restricts misleading causal conclusions.
• Simulation results show that CPC nearly matches PC in speed while significantly lowering the rate of incorrect causal arrowheads on realistic sample sizes.

Analysis of Adjacency-Faithfulness and Conservative Causal Inference

In the paper titled "Adjacency-Faithfulness and Conservative Causal Inference," authors Joseph Ramsey, Peter Spirtes, and Jiji Zhang examine the underlining assumptions in most causal discovery algorithms, focusing on the Causal Faithfulness Condition and its components. The research explores how loosening one part of this assumption, namely Adjacency-Faithfulness, impacts causality inference and elaborates on the development of a modified causal discovery algorithm, Conservative PC (CPC).

Core Discussion Points

Constraint-based causal discovery algorithms, such as the well-known PC algorithm, often rely on the Causal Faithfulness Assumption in conjunction with the Causal Markov Condition to accurately delineate causal structures from data represented by directed acyclic graphs (DAGs). The Faithfulness assumption posits that observed conditional independencies in a dataset are indicative of the underlying causal structure unless specifically entailed by the Markov Condition.

The authors dissect the Faithfulness assumption into two distinct components: Adjacency-Faithfulness and Orientation-Faithfulness. With this decomposition, the work outlines that if Adjacency-Faithfulness holds true—meaning that two adjacent variables are dependent conditional on subsets of other variables—then it is possible to test the validity of Orientation-Faithfulness.

Contribution and Claims

The authors argue that assuming only Adjacency-Faithfulness can yield valid inference results, eliminating the need to assume full Causal Faithfulness. They introduce the Conservative PC algorithm, which modifies the PC algorithm by checking Orientation-Faithfulness during the orientation phase. When this condition is proven invalid, CPC restricts the causal conclusions that would typically be drawn by the PC algorithm. However, under the scenario where full Causal Faithfulness is present, CPC's output converges to that of PC in large samples. Remarkably, simulation results demonstrate CPC's comparative efficiency, showing it runs nearly as fast as PC while producing significantly fewer incorrect causal arrowheads on realistically sized samples.

Theoretical and Practical Implications

The primary implication of this work is that causal inference algorithms can be made more reliable by strategically relaxing assumptions, in this case making the transition from comprehensive to conservative causal Faithfulness. This not only increases the robustness of causal discovery, preventing erroneous causal interpretations, but also suggests avenues for further research in refining causal inference algorithms—suggestions which hold significance in fields that require robust causal insights, such as computational epidemiology and social science analytics.

Future Directions and Considerations

The work sheds light on possible enhancements to other causal inference algorithms that operate under strict assumptions like Faithfulness. It also highlights the necessity of considering algorithmic modifications when assumptions are violated or only partially hold true. One future trajectory includes applying this relaxed assumption framework to more complex algorithms like FCI, which account for latent confounders, and exploring its impact on classrooms with stronger or novel causal assumptions.

In summary, this paper contributes to the field of causal inference by demonstrating that potential errors can be mitigated through more conservative assumptions without detriment to algorithmic efficiency. The CPC algorithm stands as an exemplar of the practical application of advanced theoretical insights to improve causal discovery.