Stochastic Optimization Algorithms for Instrumental Variable Regression with Streaming Data
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| Format: | Preprint |
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2024
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| _version_ | 1866910464112328704 |
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| author | Chen, Xuxing Roy, Abhishek Hu, Yifan Balasubramanian, Krishnakumar |
| author_facet | Chen, Xuxing Roy, Abhishek Hu, Yifan Balasubramanian, Krishnakumar |
| contents | We develop and analyze algorithms for instrumental variable regression by viewing the problem as a conditional stochastic optimization problem. In the context of least-squares instrumental variable regression, our algorithms neither require matrix inversions nor mini-batches and provides a fully online approach for performing instrumental variable regression with streaming data. When the true model is linear, we derive rates of convergence in expectation, that are of order $\mathcal{O}(\log T/T)$ and $\mathcal{O}(1/T^{1-ι})$ for any $ι>0$, respectively under the availability of two-sample and one-sample oracles, respectively, where $T$ is the number of iterations. Importantly, under the availability of the two-sample oracle, our procedure avoids explicitly modeling and estimating the relationship between confounder and the instrumental variables, demonstrating the benefit of the proposed approach over recent works based on reformulating the problem as minimax optimization problems. Numerical experiments are provided to corroborate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19463 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Optimization Algorithms for Instrumental Variable Regression with Streaming Data Chen, Xuxing Roy, Abhishek Hu, Yifan Balasubramanian, Krishnakumar Machine Learning Econometrics Optimization and Control We develop and analyze algorithms for instrumental variable regression by viewing the problem as a conditional stochastic optimization problem. In the context of least-squares instrumental variable regression, our algorithms neither require matrix inversions nor mini-batches and provides a fully online approach for performing instrumental variable regression with streaming data. When the true model is linear, we derive rates of convergence in expectation, that are of order $\mathcal{O}(\log T/T)$ and $\mathcal{O}(1/T^{1-ι})$ for any $ι>0$, respectively under the availability of two-sample and one-sample oracles, respectively, where $T$ is the number of iterations. Importantly, under the availability of the two-sample oracle, our procedure avoids explicitly modeling and estimating the relationship between confounder and the instrumental variables, demonstrating the benefit of the proposed approach over recent works based on reformulating the problem as minimax optimization problems. Numerical experiments are provided to corroborate the theoretical results. |
| title | Stochastic Optimization Algorithms for Instrumental Variable Regression with Streaming Data |
| topic | Machine Learning Econometrics Optimization and Control |
| url | https://arxiv.org/abs/2405.19463 |