Xuxing Chen, Abhishek Roy, Yifan Hu, Krishnakumar Balasubramanian
arXiv 29 May 2024 · Statistics — Machine Learning
arXiv:2405.19463 · PDF · DOI · OpenAlex · Extracted main text
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 $\mathcal{O}(1/T^{1-\iota})$ for any $\iota>0$, 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.
appendix boundary found by appendix_command · 48% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | K. Muandet, A. Mehrjou, S. K. Lee, and A. Raj (2020) Dual instrumental variable regression | 0.874 | 13 | 2 | 100% |
| 2 | B. T. Polyak and A. B. Juditsky (1992) Acceleration of stochastic approximation by averaging | 0.843 | 4 | 3 | 75% |
| 3 | R. Della Vecchia and D. Basu (2024) Stochastic online instrumental variable regression: Regrets for endogeneity and bandit feedback | 0.825 | 16 | 4 | 56% |
| 4 | A. Bennett, N. Kallus, and T. Schnabel (2019) Deep generalized method of moments for instrumental variable analysis | 0.811 | 4 | 2 | 100% |
| 5 | X. Chen, J. D. Lee, X. T. Tong, and Y. Zhang (2020) Statistical inference for model parameters in stochastic gradient descent | 0.737 | 3 | 3 | 67% |
| 6 | J. D. Angrist and J.-S. Pischke (2009) Mostly harmless econometrics: An empiricist's companion | 0.737 | 3 | 2 | 100% |
| 7 | A. Bennett, N. Kallus, X. Mao, W. Newey, V. Syrgkanis, and M. Uehara (2023) Minimax instrumental variable regression and $ l_2 $ convergence guarantees without identification or closedness | 0.737 | 3 | 2 | 100% |
| 8 | N. Dikkala, G. Lewis, L. Mackey, and V. Syrgkanis (2020) Minimax estimation of conditional moment models | 0.737 | 3 | 2 | 100% |
| 9 | L. Liao, Y.-L. Chen, Z. Yang, B. Dai, M. Kolar, and Z. Wang (2020) Provably efficient neural estimation of structural equation models: An adversarial approach | 0.737 | 3 | 2 | 100% |
| 10 | Y. Hu, S. Zhang, X. Chen, and N. He (2020) Biased stochastic first-order methods for conditional stochastic optimization and applications in meta learning | 0.693 | 5 | 1 | 100% |
Showing the top 10 of 69 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Transformers Handle Endogeneity in In-Context Linear Regression | 0.405 | 1 | 1 |
| 2 | Differentially Private Two-Stage Gradient Descent for Instrumental Variable Regression | 0.405 | 1 | 1 |
| 3 | SLIM: Stochastic Learning and Inference in Overidentified Models | 0.405 | 1 | 1 |