Title: Neural Causal Regularization under the Independence of Mechanisms Assumption
Authors: Mohammad Taha Bahadori
Krzysztof Chalupka
Edward Choi
Robert Chen
Walter F. Stewart
Jimeng Sun
Venue: ICLR 2017
Keywords: Deep learning
Applications

Abstract: Neural networks provide a powerful framework for learning the association between input and response variables and making accurate predictions. However, in many applications such as healthcare, it is important to identify causal relationships between the inputs and the response variables to be able to change the response variables by intervention on the inputs. In pursuit of models whose predictive power comes maximally from causal variables, we propose a novel causal regularizer based on the independence of mechanisms assumption. We utilize the causal regularizer to steer deep neural network architectures towards causally-interpretable solutions. We perform a large-scale analysis of electronic health records. Employing expert's judgment as the causal ground-truth, we show that our causally-regularized algorithm outperforms its L1-regularized equivalence both in predictive performance as well as causal relevance. Finally, we show that the proposed causal regularizer can be used together with representation learning algorithms to yield up to 20% improvement in the causality score of the generated hypotheses.

TL;DR: We designed a neural causal regularizer to encourage predictive models to be more causal.

Review discussion:
Algorithm 2 has notation that I find somewhat confusing.  Step 1 generates data from $p_{X,Y}$, but in my reading of the paper there is no place that actually indicates what those distributions are: I understand that Fig 1 has the graphical models, but what is the actual form of the distribution?  Does this choice influence the results?
Next, Step 2 says that the classifier is a map from measures $\mathbbm{P}_{X,Y}$ to $[0,1]$.
But how is that the input?  What form is given for the measure?  Sufficient statistics or some other form?
Alternatively, perhaps you mean that the input are samples.  If so, how many samples, and how does this affect the analysis?  This is one of the two key methodological points in the paper, and I think it warrants more specificity and mathematical detail than is currently present.
We sincerely thank you for the comments.  We have specified more details about the form of distributions for count data in Appendix A. The joint distributions $p_{X,Y}$ are generated according to Fig 1 using a sampling procedure similar to Algorithm 1. We will make sure to clarify Step 1 as you suggested.
Regarding Step 2: The inputs are not samples, the inputs are distributions. For training, the input is the joint distributions $p_{X,Y}$ sampled using Algorithm 1 and Fig 1. For testing, we use the empirical joint distributions $\hat{p}_{X,Y}$ estimated using the data. It is also possible to use a sufficient statistic or a discriminative classifier on the actual samples as Lopez-Paz et al, (2016) suggest.
While the paper provides enough detail to re-implement the proposed methods, there is no discussion as to whether the heart failure dataset will be released. This would be key for reproducibility.
The heart failure dataset is the property of Sutter Health and we are not at liberty to release it.
The method is to apply a weighted L1 regularizer where the weights are proportional to a causality score determined by some method (in this case the authors' own).  The experiments then show that selected variables on a real world data set (with no ground truth as far as I saw) have a higher causality score as regularization is increased.  This isn't so surprising.  Perhaps a more appropriate evaluation would be for some dataset where causality is known, e.g. from controlled trials.
We agree that evaluation on a dataset where the ground truth causality is known is ideal.  Unfortunately, there are not many such datasets available. We are actively working with doctors at Sutter Health to label our dataset and provide more rigorous evaluation.
Also, the main contribution of this paper is the causal regularizer, whose advantages are more easily identified in datasets with a large number of variable.
However, to our knowledge, such large datasets with true labels are not available yet.
The present submission discusses a "causal regularizer", which promotes the use of causal dependencies (X -> Y, where X is a feature of the learning problem, and Y is the target variable) in predictive models.
Similarly, such causal regularizer penalizes the use of non-causal dependencies, which can arise due to reverse causation (Y -> X) or confounding (X <- Z -> Y, where Z is a hidden confounder).
+ Overall, this submission tackles one of the most important problems in machine learning, which is to build causal models. The paper discusses and addresses this issue effectively when applied to a dataset in heart disease. In their experiments, the authors correctly identify some of the common causes of heart disease by virtue of their causal regularizer.
- The authors do not discuss the robustness of their approach with respect to choice of hyper-parameters (both describing the neural network architecture and the generative model that synthesizes artificial causal data). This seems like a crucial issue, in particular when dealing with medical data.
- The conclusions of the experimental evaluation should be discussed in greater length.
On the one hand, Figure 4.a shows that there are no differences between L1 and causal regularization in terms of predictive performance, but it is difficult to conclude if this result is statistically significant without access to error-bars.
On the other hand, Table 3 describes the qualitative differences between L1 and causal regularization.
However, this table is hard to read: How were the 30 rows selected? What does the red highlighting mean? Are these red rows some true causal features that were missed? If so, this is related to precision. What about recall? Did the causal regularization pick up many non-causal features as causal?
- Regarding causal classifiers, this paper should do a much better job at reviewing previous work.
For instance, the paper "Towards a Learning Theory of Cause-Effect Inference" from Lopez-Paz et al. is missing from the references.
However, this prior work studies many of the aspects that are hinted as novel in this submission.
In particular, the prior work of Lopez-Paz 1) introduces the concept of Mother distribution (referred as Nature hyper-prior in this submission) which explicitly factorizes the distribution over causes and mechanisms, 2) circumvented intractable likelihoods by synthesizing and training on causal data, 3) tackled the confounding case (compare Figure 1 of this submission and Appendix C of Lopez-Paz), and 4) dealt with discrete data seamlessly (such as the ChaLearn data from Section 5.3 in Lopez-Paz).
On a positive note, this is a well-written paper that addresses the important, under-appreciated problem of incorporating causal reasoning into machine learning. On a negative note, the novelty of the technical contributions is modest and the qualitative evaluation of the results could be greatly extended.
In short, I am leaning slightly towards acceptance.
We would like to sincerely thank you for the detailed and constructive review.  We will make sure to address all of your comments and improve the quality of the paper.
Also, two days ago we uploaded a revision that addresses some of your comments on related works. In Section 2.1, we included the related works on causal discovery via independence of mechanisms assumption and clarified that other methods (such as Lopez-Paz’s work) could also be used to construction of our regularizer in Section 2.2.  At the end of Section 2.2, we describe the novelty of our proposed regularizer given the existing literature.
We will write a more elaborate response after addressing your comments and uploading a new revision of the paper.
We would like to thank you for your constructive feedback.  Your feedback allowed us to make a major revision to the paper.
We rewrote the paper with more detailed discussion of the related works.  We improved the evaluation by including a publicly available dataset and also ground truth causality evaluation.
Please see the other major improvements to the paper listed in our revision note.
The authors extend their method of causal discovery (Chalupka et al 2016) to include assumptions about sparsity via regularization.  They apply this extension to an interesting private dataset from Sutter Health.
While an interesting direction, I found the presentation somewhat confused, the methodological novelty smaller than the bulk of ICLR works, and the central results (or perhaps data; see below) inadequate to address questions of causality.
First, I found the presentation somewhat unclear.  The paper at some points seems to be entirely focused on healthcare data, at other points it uses it as a motivating example, and at other points it is neglected.
Also, algorithm 1 seems unreferenced, and I'm not entirely sure why it is needed.  Figure 2 is not needed for this community.  The key methodological advance in this work appears in section 2.1 (Causal regularizer), but it is introduced amidst toy examples and without clear terminology or standard methodological assumptions/build-up.  In Section 3.1 (bottom of first paragraph), key data and results seem to be relegated to the appendices.
Thus overall the paper read rather haphazardly.
Finally, there seems to be an assumption throughout of fairly intimate familiarity with the Cholupka preprint, which i think should be avoided.  This paper should stand alone.
Second, while the technical contributions/novelty are not a focus of the paper's presentation, I am concerned by the lack of methodological advance.  Essentially a regularization objective is added to the previous method, which of itself is not a bad idea, but I can't point to a technical novelty in the paper that the community can not do without.
Third, fundamentally i don't see how the experiments address the central question of causality; they show regularization behaving as expected (or rather, influencing weights as expected), but I don't think we really have any meaningful quantitative evidence that causality has been learned.  This was briefly discussed (see "ground truth causality?" and the response below).  I appreciate the technical challenges/impossibility of having such a dataset, but if that's the case, then I think this work is premature, since there is no way to really validate.
Overall it's clearly a sincere effort, but I found it wanting in terms of a few critical areas.
We would like to thank you for your constructive feedback.  Your feedback allowed us to make a major revision to the paper.
We made a complete overhaul to the write-up and also additional novel methodology in Section 2.3.  Now you can easily see the novelty of the work in Sections 2.2 and 2.3.
We deleted the figure that you pointed out and included more insightful figures in Figure 2.
Regarding the ground truth causality, we hired a clinical expert to provide us the ground truth causality labels (Table 2). The results strongly confirm the key claims of the paper about the performance of causal regularizer.
This paper proposes to use a causality score to weight a sparsity regularizer.  In that way, selected variables trade off between being causal and discriminative.  The framework is primarily evaluated on a proprietary health dataset.
While the dataset does give a good motivation to the problem setting, the paper falls a bit short for ICLR due to the lack of additional controlled experiments, relatively straightforward methodology (given the approach of Chalupka et al., arXiv Preprint, 2016, which is a more interesting paper from a technical perspective), and paucity of theoretical motivation.
At the core of this paper, the approach is effectively to weight a sparsity regularizer so that "causal" variables (as determined by a separate objective) are more likely to be selected.  This is generally a good idea, but we do not get a proper validation of this from the experiments as ground truth is absent.  A theorem on identifiability of causal+discriminative variables from a data sample combined with adequate synthetic experiments would have probably been sufficient, for example, to push the paper towards accept from a technical perspective, but as it is, it is lacking in insight and reproducibility.
We would like to thank you for your constructive feedback.  Your feedback allowed us to make a major revision to the paper.
As we listed in the revision notes, in the revised paper we added experiments on a publicly available dataset (MIMIC III) and even preprocessed using a publicly available script. Now, half of the results in Table 1 and Figure 3 are completely reproducible.
Furthermore, we hired a clinical expert to provide us the ground truth causality labels (Table 2). The results strongly confirm the key claims of the paper about the performance of causal regularizer compared to the two step procedure.
Finally, we added another use case for causal regularizer in Section 2.3 and reorganized the section to highlight novel contributions of this paper compared to (Chalupka et al 2016) and (Lopez-Paz et al, 2016)
We made a major revision to the paper.  Here is the summary of the main changes:
Experiments:
-- Providing **ground truth causality** evaluation (by hiring Robert Chen, a clinical expert). (Figure 1, Table 2) The results show a significant gain in causality discovery using the proposed method.
-- Including a new **publicly available dataset** (MIMIC III) to ensure reproducibility of the results. (Table 1 and Figure 4)
-- Adding standard deviation to the results.
Novel methodology:
-- Providing a neural network architecture that allows multivariate causal hypothesis generation, see Section 2.3 and Figure 2.b.
-- Providing the ground truth causality evaluation for the causal hypotheses generated by our algorithm. (Figure 5b)
Writeup:
-- Adding more discussion on the related works (Sections 2.1 and 2.2).
---- In the introduction and Section 2.2 we clearly describe the novelty of this paper with respect to the papers listed by David Lopez-Paz and the reviewers.
-- Revising the background section 2.1 and making it both more accessible and more mathematically precise.
-- Adding new visualizations in Figure 2 and removing diagrams that didn’t help delivering the concepts.
-- Restructuring the methodology section. Now Section 2.2 only discusses the proposed causal regularizer and Section 2.3 describes its combination with neural networks.
-- Moving the experimental results on the causality detection (and other extra results) to Appendix A.1, to allow space for evaluation of the main results of the paper.
-- Finally, we revised the introduction accordingly.

Meta-review:
role: PC
data: comment: The reviewers pointed out several issues with the paper, and all recommended rejection. The revision seems to not have been enough to change their minds.

Decision: Reject