Since Faithfulness Fails: The Performance Limits of Neural Causal Discovery

Authors: Mateusz Olko, Mateusz Gajewski, Joanna Wojciechowska, Łukasz Kuciński, Mikołaj Morzy, Piotr Sankowski, Piotr Miłoś
Primary area: causal reasoning
Keywords: causal discovery, faithfulness assumption, neural networks

Abstract:
Neural causal discovery methods have recently improved in terms of scalability and computational efficiency.
However, there are still opportunities for improving their accuracy in uncovering causal structures.
We argue that the key obstacle in unlocking this potential is the faithfulness assumption, commonly used by contemporary neural approaches. We show that this assumption, which is often not satisfied in real-world or synthetic datasets, limits the effectiveness of existing methods. We evaluate
the impact of
faithfulness violations both qualitatively and quantitatively and provide a unified evaluation framework to facilitate further research.

Decision: reject
Reviewer scores: 6, 5, 5, 6

Reviews and discussion:
<thread>
creation date:
1730369564160

thread_type:
official_review

<thread_object>
creator: reviewer_cv1a

<content>
summary:
The paper presents the idea that the ''faithfulness assumption" is holding back the improvements in the neural causal discovery research. The work starts with empirically demonstrating the strenghts and limitations of neural causal discovery. To this end, a benchmark is proposed where several of the discovery algorithms are evaluated.  Then a degree of faithfulness metric is proposed that is helpful to estimate to what degree does faithfulness effect the discovery algorithms.

strengths:
1. The premise is really interesting. Identifying the faithfulness assumption as the main culprit is an important hypothesis that can have wide ranging impact.

2. The paper is relatively well written.

weaknesses:
There are several issues with the paper that forces me to go with a lower rating.

1. Although the premise is interesting, the overall work does not justify the premise. For example, using a AUC-ROC curve to measure faithfulness is not very well justified. Also quantifying the conditional dependecies by a correlation coefficient is not very innovative/interesting. 

2. The works talks about why such assumptions are a problem for real world datasets, but the experimental evaluations are on synthetic data sets. This kind of defeats the message.

3. The NN-opt method seems to pretty expensive since all possible DAG's are being evaluated.

4. In Fig 2, SDCD and Bayes DAF do show a downward trend so maybe more evaluations are required before claiming that there is no improvement in the ESHD metric.

5. Spell check required. Eg: Masuring -> Measuring in heading of Section 4.

questions:
Please look at the weaknesses section. Furthermore,

1. Were there any ablation studies conducted for the neural networks as functional aprroximators?

2. I do not see the point of Fig 1 to be honest. It gives no specific information.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730639262390

thread_type:
official_review

<thread_object>
creator: reviewer_ycc2

<content>
summary:
This paper has claimed that progress in causal discovery requires moving beyond the faithfulness assumption. The experiments shows that the violation of faithfulness would degrade performance. To clearly quantify this phenomenon, a metric called DeFaith has been proposed. Also, as the increase of sample size, the performance of different methods, including DCDI, BayseDAG, DiBS, SCCD, don’t show improvement or even show degraded performance. To investigate the limits of different socre-based neural causal discovery methods, an algorithm called NN-opt has been proposed which consists two step. Through NN-opt, the upper bound of the neural method could be estimated.

strengths:
1. This paper touches some important theoretical aspects of neural causal discovery.
2. Several ordinary causal approaches are compared.

weaknesses:
1. The theoretical analysis can be built more in depth to justify the arguements of the paper.

questions:
Q1:In the structure evaluation, Expected SHD between CPDAGs and Expected F1-Score between CPDAGs have been defined. Compared to other metrics such as SHD and SID, is there any strength or reason to use them?

Q2:DeFaith is proposed to evaluated the faithfulness, but could this metric accurately describe the change of the faithfulness? Could you give more theoretical analysis about the reality between the faithfulness and DeFaith? It is better if this quantification can be justified to be more theoretically "close" to the faithfulness.

Q3:As mentioned before, NN-opt could compute the upper bound of specific methods. In step 2, which is exhaustive graph search, it is not feasible in practice. Is there any way to improve the method to make it practiced?

Q4:In this paper, several methods have been evaluated to search the upper bound of these methods using different sample size and neural structures. From the aspect of experiments, the methods evaluated in the paper may only include some typical ones among all methods and it’s more persuasive to compare more socre-based neural causal discovery methods. Could you give some reason of the selection of the four methods?
</content>
</thread_object>

</thread>
<thread>
creation date:
1730783624399

thread_type:
official_review

<thread_object>
creator: reviewer_cqrq

<content>
summary:
This paper experimentally demonstrates that violating the faithfulness assumption is the key obstacle in improving the performance of existing neural causal discovery methods. In this paper, the authors introduce a metric to measure the degree of faithfulness violation, and also proposed a method to compute an experimental bound on the causal discovery performance.

strengths:
- I totally agree with the authors on the assertion that faithfulness violations might be the key reason why the performance within the current causal discovery paradigm is limited to a large extent. I am happy to see the experimental support presented in this work.
    
- The proposed metric of faithfulness violations also makes sense
    
- The paper is well organized in a logical manner, and is easy to follow.

weaknesses:
- The analyses presented in the paper are only experimental, lacking a theoretical foundation. Although they provide some insights, it might be not convincing enough to generalize to other scenarios.
    
- The proposed method to compute experimental upper bound is highly unlikely to scale up.

questions:
- Why assuming additive noise SCMs in the paper?
    
- How general is the proposed faithfulness metric? At what conditions does it work?
    
- Why not choosing NOTEARS or its variants as baselines? I think NOTEARS might be one of the most well-known neural causal discovery methods?
    
- Since MLPs have universally strong fitting abilities, the loss easily converges to zero or a very small value when training a network for each parent set. In this case, it is possible that the log-likelihood losses of many DAGs lead to zero or a very small value or have very similar value. If so, how to identify the true DAG?
</content>
</thread_object>

</thread>
<thread>
creation date:
1730960769748

thread_type:
official_review

<thread_object>
creator: reviewer_yhzg

<content>
summary:
This paper posits that the primary obstacle in neural causal discovery is the faithfulness assumption frequently used by modern neural approaches. It examines the impact of violations of this assumption both qualitatively and quantitatively, and provides a unified evaluation framework to facilitate further research.

strengths:
- The main claim of this work is that progress in causal discovery requires moving beyond the faithfulness assumption, which is a reasonable standpoint. The key experimental findings are:
 >- despite advancements in causal discovery over the past few years, $ESHD_{CPDAG}$ and $F1-Score_{CPDAG}$ metrics do not improve significantly. 
>-  structure discovery accuracy does not scale with the amount of data. 
>-  variations in MLP architecture have minimal impact on performance.

-  develop techniques to measure how faithfulness violations degrade performance (Figure 4 is particularly interesting) and set an
upper bound for current benchmarks.

-  The paper is well-written.

weaknesses:
- Line 71 : $U_{i}$ is assumed to be 1-dimensional.  Justify.
- Please justify the additive noise assumption. 
- > Faithfulness assumption can be violated, for example, in a situation when paths cancel each other effects out, leading to statistical independence despite an existing causal relationship. 

**Give concrete example**
 - Expected SHD between CPDAGs has been discussed; there is no discussion about $F1-Score_{CPDAG}$
 -  Why do Table 1 and Section 3.2  miss the result on ER(5, 1)? 
 - why do you exclude *DIFFUSION MODELS FOR CAUSAL DISCOVERY
VIA TOPOLOGICAL ORDERING* in your analysis? 

- > To provide a comprehensive evaluation, we explored architectures with 1, 2, and 3 layers, configured
with 4, 8, and 16 hidden units.

**why do you think this is sufficient to conclude *variations in MLP architecture have minimal impact on performance* ?**

- The faithfulness metric, denoted DeFaith needs more detailed discussion. For example, 
>  To address this, we introduce a degree of faithfulness metric, denoted DeFaith, to measure how well statistical dependencies correspond to the true graph’s d-separation properties. Inspired by Zhang & Spirtes (2003), we use Spearman’s rank correlation coefficient to quantify the conditional dependencies in the dataset. We define a predictor of d-separation based on the coefficient.

**Please clearly state what is the predictor here.**
**More discussion is needed around the quality of this predictor itself**.

- The paper does not address how to design neural causal discovery methods without the faithfulness assumption.

questions:
Please see Weaknesses
</content>
</thread_object>

</thread>
<thread>
creation date:
1732201253932

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
General response to the Reviewers

comment:
We would like to thank all Reviewers for taking the time to review our work and providing us with insightful feedback. We are glad that the Reviewers appreciated the strengths of our paper, the importance of the subject (Reviewer yCC2, CV1a), the straightforward and interesting formulation of the research problem (Reviewers YhZG, CQrQ, yCC2, CV1a), the technique to measure faithfulness violations (Reviewers YhZG, CQrQ). We are glad to learn that the paper is well-written (Reviewers YhZG, CQrQ, CV1a), easy to follow (Reviewer CQrQ), and that the work is well presented (Reviewer yCC2).
We have carefully considered all feedback provided by the Reviewers and prepared a new revision of the paper based on it. New changes are marked with the red color.
We have identified a set of common concerns that we would like to address jointly:

**Justification for the selection of methods**

Reviewers CQrQ and  yCC2 raised concerns about the suite of methods (DCDI, SDCD, DiBS and BayesDAG) used in our work. We claim that the selected suit adequately covers also NO-TEARS, NO-BEARS, NO-CURL, GRAN-DAG, SCORE, DAGMA, and DCDFG. Below, we provide a detailed explanation, which is now included in Appendix E and hinted at in Section 2. 

NO-TEARS is the first method to use augmented Lagrangian and differentiable constraints to enforce DAGness. However, suggested formulation entangles functional and structural parameters, making NO-TEARS applicable only with linear models or restricted neural networks. The NO-TEARS method was improved in GRAN-DAG (introduces separate adjacency matrix and sampling based on gumbel softmax) and then in DCDI (accounts for interventional data). We chose to use DCDI as it the most developed method in this line of work and has clean implementation.

An interesting line of work shows articles introducing methods such as NO-BEARS and DAGMA, that were focused on improving the acyclicity constraint introduced in NO-TEARS, all proposed constraints were unified in the SDCD paper, and a new constraint was proposed, that was shown to perform the best. Additionally, SDCD is also compared against SCORE and DCDFG again presenting better performance.

The two other methods are from the class of Bayesian approaches. DiBS method is selected as a Bayesian approach that uses classic NO-TEARS-based regularization embedded in its prior. The BayesDAG is based on the NO-CURL parametrization of DAGs and provides improvements to the optimization pipeline (uses MCMC instead of SVGD).

We argue that this selection of four methods summarizes various research directions and improvements explored in neural causal discovery over the last four years and well represents the spectrum of existing approaches. If the Reviewers think this comparison is too narrow, we kindly ask the Reviewer to specifically name additional methods that they think it is essential we compare against.


**Clarifications regarding NN-opt efficiency and applicability**

To clarify, NN-opt is a brute force technique intended to be as powerful as possible in causal discovery. The price to pay is efficiency. NN-opt is helpful as an upper-bound benchmark but is not practical to use. To avoid confusion, we put additional information about this in Section 5.

To develop NN-opt we identify two key elements (1) modeling functional relationships and (2) search over the dag space. In practical methods, these are intertwined and solved in an approximate fashion. NN–opt method disentangles those two objectives trading additional compute for more accurate results. 
1. The modeling of functional relationships was done by training an ensemble model for each parent set. Such an approach provides a more robust approximation of the score. 
2. The exhaustive search removes challenges related to the optimization scheme
</content>
</thread_object>

</thread>
<thread>
creation date:
1732794981945

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
Manuscript Revision and Follow-Up on Reviewer's Comments

comment:
We sincerely thank Reviewer CV1a for their valuable feedback and for engaging in the discussion. Based on their suggestions, we have made further improvements to the manuscript.

In the revised version, we have included an additional experiment on real-world structures to further substantiate our findings. Additionally, we extended Figure 2 with results on 25K samples. We recomputed all results for DiBS on graphs ER(10,2) as we realized that the set of hyperparameters used previously was not optimal as one of them was incorrectly introduced into the configuration file. 

Despite these updates, the main conclusion from section 3 remains unchanged. The method's performance remains unsatisfactory and there is no consistent pattern of improvement in the ESHD_CPDAG metric as observational sample size increases — this holds true for both synthetic and real-world structures. Section 3 has been updated accordingly to reflect the findings from the new experiments.

We kindly invite Reviewers YhZG, CQrQ, and yCC2 to share their responses to our rebuttal. We are happy to provide additional clarifications or further improvements to the paper if needed. Alternatively, if the reviewers are satisfied with our responses and the changes made so far, we respectfully request that they consider revising their scores.
</content>
</thread_object>

</thread>
<thread>
creation date:
1733308000021

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
Final Thank You and Rebuttal Summary

comment:
Once again, we would like to express our gratitude for the time and effort the Reviewers took to review our work and for the useful feedback provided. With the Reviewers' help we have been able to provide numerous improvements to the manuscript:
* We included additional experiments to support results from section 3, as suggested by Reviewers YhZG and CV1a. We provided results for benchmarking in higher sample sizes, more network architecture ablations, and additional results on real-world structures. All new results confirm our observations.
* We improved the descriptions of the DeFaith measure (Section 4), NN-opt method (Section 5), and metrics explanation (Section 2)  based on the provided comments.
* By the suggestion of the Reviewers YhZG, CQrQ, and yCC2, we provided additional justification for the selection of methods and metrics and an example of faithfulness violation in Appendices A, D, and E.

We thank the Reviewers YhZG and CV1a for acknowledging that applied changes significantly improved the overall quality of the paper by increasing their scores!

The Reviewer yCC2 signified the need for theoretical grounding of the DeFaith measure. We have just provided a detailed response explaining the theoretical foundation of our approach. We hope the answer is exhaustive, and we will include a similar explanation in the camera-ready version.

We have carefully considered all comments of the Reviewer CQrQ and provided detailed responses for all of them. We hope we have addressed all their concerns, though we regret that we weren't given the opportunity to correct any ambiguities in a discussion.

Thank you for your thoughtful comments and suggestions, which have significantly enhanced the quality of our paper. We hope that the improved manuscript meets the expectations of the Reviewers and the broader research community.
</content>
</thread_object>

</thread>


Metareview:
metareview:
The paper investigates the impact of faithfulness violation on current causal learning methods. The motivations for this assumption are clear; what happens when it fails (and to a lesser extent, why) is explored in the paper. The study focuses on neural causal learning methods.

Two lessons learned are: i) the data amount does help to some extent (then the performance reaches a plateau); ii) the complexity of the neural architecture does not matter much.
One interesting contribution is a new indicator, measuring the faithfulness violation, called DeFaith. This indicator is shown to be correlated to the performance (causal graph identification). Note however that this indicator requires the ground truth to be known.