Transformers Handle Endogeneity in In-Context Linear Regression

• URL: http://arxiv.org/abs/2410.01265v1
• Date: Wed, 2 Oct 2024 06:21:04 GMT
• Title: Transformers Handle Endogeneity in In-Context Linear Regression
• Authors: Haodong Liang, Krishnakumar Balasubramanian, Lifeng Lai,
• Abstract summary: We show that transformers inherently possess a mechanism to handle endogeneity effectively using instrumental variables (IV) 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.
• Score: 34.458004744956334
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $(\textsf{2SLS})$ 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 $\textsf{2SLS}$ method, in the presence of endogeneity.

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