Transformers Handle Endogeneity in In-Context Linear Regression
endogeneity;instrumental variables;transformers;bi-level gradient descent
Yes
No ethics review needed.
I want to caveat this review by saying that I have flagged to the AC that this is not my area of expertise.

I wonder how this work helps one to understand what capabilities a transformer should / should not be capable of? Can we say something more concrete / general around what class of functions we can argue that a transformer should be able to solve? How does this relate to larger models ?
I want to caveat this review by saying that I have flagged to the AC that this is not my area of expertise.

The paper seems interesting: it extends the theoretical analysis done in previous work that looks at the class of functions that transformers can learn (e.g. simple linear regression) to a more complex set -- those with endogeneity and corresponding instrument variables. The authors show that transformers can learn this function and do as well as the direct solvers in most cases and potentially better in more challenging cases. They supplement this with a theoretical analysis.
The paper extends the theoretical analysis done in previous work that looks at the class of functions that transformers can learn (e.g. simple linear regression) to a more complex set -- those with endogeneity and corresponding instrument variables. The authors show that transformers can learn this function and do as well as the direct solvers in most cases and potentially better in more challenging cases. They supplement this with a theoretical analysis.
I want to caveat this review by saying that I have flagged to the AC that this is not my area of expertise.

I do not know enough about this area to understand the potential flaws in their statements / etc or more subtle points.
At a broad level, their intro / overview makes sense and seems convincing.
Yes
No ethics review needed.
Please refer to the weaknesses section.
I am not familiar with IV regression and endogeneity, so I haven't reviewed the mathematical accuracy of the theorem. My comments are based solely on a basic understanding of the motivation, overall contribution, and presentation. Please consider them with low weights.

Overall, I find the paper well-motivated, with clear writing. The background information and literature review appear thorough.

Understanding the mechanism of the Transformer could be valuable for advancing future research in this area.
This paper first analyzes how to use IV regression for endogeneity, where the IV regression is estimated with 2SLS. Then, an error bound is proposed for this process. Furthermore, the paper shows that the transformer can achieve the gradient-based 2SLS for in-context linear regression.
I understand that theoretical analysis requires specific assumptions. I am, however, curious whether it might be possible to extend the theoretical analysis to the non-linear case, as most real-world scenarios tend to be non-linear.

Additionally, could you provide an example of real-world applications where the proposed analysis could be beneficial? If such examples exist, is it feasible to validate the analysis experimentally?
Yes
No ethics review needed.
(1) How does the proposed transformer model handle cases with highly correlated instruments? In many practical applications, instrumental variables may exhibit multicollinearity, which could impact the model's stability and coefficient estimates. Could the authors clarify whether the model’s training or architecture includes mechanisms to address such cases?

(2) What led to the choice of hyperparameters in the pretraining scheme? The paper presents a theoretical guarantee of minimal excess loss but does not detail the rationale behind the selection of specific hyperparameters, such as learning rates or number of transformer layers. Could the authors provide insights or guidelines on choosing these parameters for optimal performance?

(3) How sensitive is the model to changes in the strength of endogeneity? While the experiments demonstrate robustness to varying IV strengths, it would be valuable to understand if there is a threshold or particular cases where the transformer’s performance degrades. Could the authors elaborate on the model's sensitivity to different degrees of endogeneity?
(1) This paper creatively combines transformer architectures with econometric techniques, specifically instrumental variables, to address endogeneity—a novel approach that extends transformers' applicability beyond traditional machine learning domains.

(2) The authors provide rigorous theoretical backing, including a bi-level optimization framework, and offer non-asymptotic error bounds, supporting their claims with comprehensive experiments that validate the model's performance against standard benchmarks like 2SLS.

(3)  By demonstrating that transformers can not only handle endogeneity but also generalize to complex scenarios (e.g., weak and non-linear IV), this work highlights the potential of transformers as a robust tool in econometrics, broadening the scope of in-context learning applications.
The paper investigates the ability of transformers to address endogeneity in in-context linear regression, proposing that transformers can emulate the two-stage least squares (2SLS) method through gradient-based optimization. Key contributions include demonstrating how transformers can handle endogeneity using instrumental variables, proposing an in-context pretraining scheme with theoretical guarantees for minimal excess loss, and showcasing robust performance in various endogeneity scenarios, including weak and non-linear instrumental variables​.
(1) The paper provides strong theoretical foundations but lacks practical guidance for implementation. More details on the parameter settings, model configurations, and optimization process would enhance reproducibility and help readers better understand how to apply the proposed method.

(2) While the theoretical contributions are thorough, the presentation is complex and could benefit from simplification or visual aids. This would make the bi-level optimization framework and convergence properties more accessible to a broader audience.

(3)  The paper does not address the scalability of the proposed transformer model for handling endogeneity. Including an analysis of computational efficiency or memory requirements would help clarify its suitability for larger datasets or higher-dimensional problems.
Transformers handle endogeneity in in-context linear regression by implementing gradient-based instrumental variable regression.
@inproceedings{
anonymous2024transformers,
title={Transformers Handle Endogeneity in In-Context Linear Regression},
author={Anonymous},
booktitle={Submitted to The Thirteenth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=QfhU3ZC2g1},
note={under review}
}
We explore the capability of transformers to address endogeneity in in-context linear regression. Our main finding is that transformers inherently possess a mechanism to handle endogeneity effectively using instrumental variables (IV). First, we demonstrate that the transformer architecture can emulate a gradient-based bi-level optimization procedure that converges to the widely used two-stage least squares (2SLS) solution at an exponential rate. Next, we propose an in-context pretraining scheme and provide theoretical guarantees showing that the global minimizer of the pre-training loss achieves a small excess loss. Our extensive experiments validate these theoretical findings, showing that the trained transformer provides more robust and reliable in-context predictions and coefficient estimates than the 2SLS method, in the presence of endogeneity.
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endogeneity instrumental variables transformers bi-level gradient descent
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Transformers Handle Endogeneity in In-Context Linear Regression
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