CausalStock: Deep End-to-end Causal Discovery for News-driven Multi-stock Movement Prediction

Thank you very much for your valuable suggestions! We will try our best to tackle the concerns one by one.

(1) Comparision with the traditional causal discovery method and the correlation matrix

• We greatly appreciate your insightful comments! Following your suggestion, we compare our discovered causal matrix with the matrix calculated by the traditional causal discovery methods and the correlation matrix. The performance results are shown as follows, which indicates that our causal discovery module has a significant advantage over others.

• Compared to traditional causal methods, our integrated causal discovery and prediction modules form an end-to-end deep learning framework, which can constrain the discovered causal graph by simulating the data generation process. In comparison to correlation-based methods, causal relationships are more suitable for representing stock relationships.

(2) Complexity analysis and cost time comparison.

• Thanks for pointing this out. We made a rough estimate of the baselines' complexity on the multi-stock movement prediction task from two perspectives: running time and training cost FLOPs corresponding to the time complexity and the number of parameters corresponding to the space complexity.
• We leverage an NVIDIA GeForce RTX 3090 and all the parameter settings of baselines follow the original papers.

The complexity and prediction accuracy results of our method and baselines are shown in the following table.

• From the table above, it can be seen that we can achieve good performance with comparable complexity.

(3) About Figure 2

• We have shown the main structure and the most contributive part details of our model in the submitted version.
• Thank you for your reminder. We have made a more comprehensive model structure in the attached pdf file.

(4) About the learning of causal graph

• The ground truth causal graph of the stock market is unknown, so we need certain theoretical guarantees to approximate the true causal relation. Under the current setup, we can theoretically prove that this learning process can converge to the true causal graph.

• Validity of variational objective:

  • Our model holds the following assumptions: Causal Markov Property, Minimality and Structural Identifiability, Correct Specification, Causal Sufficiency, and Regularity of log-likelihood (see Appendix B for a detailed description).
  • If we further assume that there is no model misspecification, then the Maximum Likelihood Estimation solution $\theta'$ and the variational posterior distribution of $G$ satisfies $q'_\phi(G)=\sigma(G=G')$ by optimizing the ELBO term with infinite data, where $G'$ is a unique graph.
  • In particular, $G'=G^*$ and $p_\theta'(X;G')=p(X;G^*)$, where $G^*$ is the ground truth graph and $p(X;G^*)$ is the true data generating distribution. Please find reference [1] for a more detailed proof.

[1] Wenbo Gong, Joel Jennings, Cheng Zhang, and Nick Pawlowski. Rhino: Deep causal temporal relationship learning with history-dependent noise. arXiv preprint arXiv:2210.14706, 2022.

(5) About the sudden market shifts or unprecedented events

• Thanks for this constructive comment! Our model could handle sudden market shifts or unprecedented events from the following perspectives:

  • Incorporating News to Capture Market Dynamics: One of the primary purposes of incorporating news into our model is to capture real-time market dynamics. News data can reflect market changes and sudden events promptly. By processing and analyzing news information quickly, our model can rapidly adjust its predictions based on new information. This allows the model to react swiftly and accurately to sudden market shifts.

  • Causal Relationships to Respond to Sudden Events: Our model's ability to learn causal relationships helps it respond effectively to sudden events. For example, if negative news is detected, the causal relationships in the model can identify which stocks might be affected and react accordingly. This mechanism ensures that the model not only considers the directly impacted stocks but also identifies related stocks that might be influenced, providing a comprehensive view of market dynamics.

  • Adjusting Priors to Reflect Changes in Causal Relationships: If a sudden event affects the causal relationships between stocks, such as a company ending a partnership, our model can adjust by incorporating the new pre-defined knowledge into the priors. This allows the causal graph to be dynamically updated to reflect the latest market structure and relationship changes, maintaining the accuracy and relevance of the predictions.

• Thus, our model could effectively handle sudden market shifts and unprecedented events.

We would appreciate it very much if you could raise the score if the concerns are solved. Thank you!

Thank you very much for the insightful and constructive comments! We sincerely appreciate the suggestions to improve our submission. We will address all raised concerns one by one.

(1) About the performance without graph module

• Following your suggestion, we ablate the graph module and compare it with our method to explore the value of our causal discovery module. Besides, we compare our causal discovery module with other traditional causal discovery methods, i.e. PC and GES, and the Spearman correlation matrix. The performance results are shown as follows, which indicates that our causal discovery module has a significant advantage over others.

(2) About the ablation results

• Thanks for pointing this out! We have noticed that two ablation results of two datasets were mistakenly swapped in our presentation of the results. We sincerely apologize for this oversight, and we have now corrected it in the following table.

Thank you for your thorough review again. We will be more diligent in our checks to prevent similar errors in the future. We would appreciate it very much if you could raise the score if the concerns are solved. Thank you!

Thanks for the new results and correction. I raise my score accordingly. Please include the ablation study in the new version.

Thank you very much for your valuable suggestions and your encouraging comments! We will try our best to tackle the concerns.

(1) If sparseness constraints used in the loss function?

• Thank you for the question. We use sparseness constraints in the loss function. These constraints are included in the Evidence Lower Bound (ELBO) term, as shown in Equation 13. The final loss function (Equation 14) includes the ELBO term (Equation 13) and the BCE loss term (Equation 13).

(2) About the correlation calculation in Section 4.4

• The causal strength graph $\hat{G}$ is designed to evaluate the causal strength. It has the same size as the causal graph $G$, with each position being a learnable parameter. After averaging the causal strength graph across all time lags, we obtain a matrix that indicates the magnitude of the causal influence of each company on other companies. Figure 3(a) is an example of such a matrix. Then the correlation in Section 4.4 and Appendix D is calculated by Spearman’s rank correlation coefficient between this matrix and the market values of the corresponding company to explore the explainability.

(3) About the Causal Markov Property

• The definition of Causal Markov Property [1] is as follows: Given a directed acyclic graph (DAG) $G$ and a joint distribution $p$, this distribution is said to satisfy Causal Markov Property w.r.t. the DAG $G$ if each variable is independent of its non-descendants given its parents. It is different from the traditional temporal Markov Property.

• Under our setup, all the historical nodes we considered are served as the parent nodes of the target nodes. Specifically, in our lag-dependent temporal causal mechanism, even though we set the causal nodes are lag-dependent, once all of them are given, the target nodes are independent of the other unmodeled factors. This is a common assumption in the field of causal discovery, and our model satisfies this assumption.

[1] Jonas Peters, Dominik Janzing, and Bernhard Scho ̈lkopf. Elements of causal inference: foundations and learning algorithms. The MIT Press, 2017.

(4) About the visualization of the learned causal graphs and news cases

• We have provided a visualization of the learned causal graph and some news cases in Figure 3.
• For a more detailed illustration, if negative news is detected, then the causal relationships in the model can identify which stocks might be affected and react accordingly by passing the information extracted from the news, which is empowered by the integration of news and causal discovery.

We would appreciate it very much if you could raise the score if the concerns are solved. Thank you!

Thank you very much for your valuable suggestions! We will try our best to tackle the concerns one by one.

(1) About the choice reason of Bernoulli distribution

• Thank you for the question. The essence of causal relationships is determining whether a change in one variable directly causes a change in another variable. This binary decision process can naturally be modeled using the Bernoulli distribution. For each causal link, we need to determine whether it exists, which is a typical binary problem—either the causal link exists (represented by 1) or it does not exist (represented by 0). The Bernoulli distribution is used to describe this type of binary random variable, making it very suitable for our needs.

(2) About the independence assumption of causal edges

• While each causal link is not completely independent, in our proposed Lag-dependent temporal causal discovery, the causal links are conditionally dependent on temporal lags, as shown in Equation 5 of our paper. However, for different stocks, the causal links are indeed assumed to be independent, which simplifies computational complexity, making the model more efficient to train and infer by parallel computation, especially for large-scale stock sets. We also consider the dependent relationships among stocks, such as sector-specific relationships like you mentioned. We included a plug-and-play option in the prior, as shown in Equation 4, allowing the model to incorporate trusted prior knowledge, such as industry knowledge or company collaboration information. This flexibility enables the model to capture more complex dependencies when such information is available.

(3) About the time-varied causal graph

• Thanks for your constructive comment. The ground truth causal graph of the stock market is unknown, so we need certain theoretical guarantees to approximate the true causal relation. Under the current setup, We can theoretically prove that this time-invaried causal learning mechanism converges to the true causal graph (see Appendix B).

• The point you raised is highly valuable in practical applications. In the future, we can consider adopting meta-learning or incremental learning training methods to update the causal graph iteratively. This way, the model can continue to learn and update based on new data in practical applications, thereby reflecting the dynamic causal relation changes in the market.

(4) About the varied number of news

• The number and distribution of news articles are related to the dataset. Below are the statistics of our news datasets:

• For the absence of news data, CausalStock leverages only the price data to construct the causal graph (see Appendix B for details) and subsequently integrates the discovered causal relations and price data for predictions. Even without news data, our model can effectively perform causal inference and make predictions using price data alone.

• When there are multiple news articles for a particular stock within a given look-back window, we employ LLMs to filter and score the articles. From this process, we retain up to a maximum number of 30 most relevant articles per day to ensure that the model receives focused and informative input. These selected articles are then encoded and fed into the network, maintaining the model's effectiveness and accuracy in handling multiple news sources.

(5) About the simultaneous modeling of the existence and non-existence likelihood

• We model the existence and non-existence likelihood simultaneously, which ensures greater flexibility and could avoid the constrained optimization. Besides, we also perform the idea the reviewer mentioned: only model the causal link existence logits and operate the Sigmoid function to obtain the link probability. We compare these two methods and the results are as follows:

(6) About limitations and future work

Thanks for your constructive suggestions! We have deeply considered it and come up with new thinking results of the limitations.

• This paper explores a method that discovers causal relations based on theoretical considerations. In the future, we could try to adopt meta-learning or incremental learning training methods to update the causal graph iteratively, i.e. explore the time-varied causal graph.

• While the Bernoulli distribution is suitable for determining whether a causal link exists, if we want to further explore the multi-level nature of causal relationships, more complex distributions might be needed. In the future, we could improve the model in this way.

We would appreciate it very much if you could raise the score if the concerns are solved. Thank you!

We sincerely thank you for your encouraging comments! All the additional experimental results will be included in the revision.

If our response has addressed your concerns, we would greatly appreciate it if you could kindly consider raising the score to support our work. Thank you for your valuable feedback and supportive encouragement!