Haodong Liang, Yanhao Jin, Krishnakumar Balasubramanian, Lifeng Lai
arXiv 26 Sep 2025 · Statistics — Machine Learning
arXiv:2509.22794 · PDF · DOI · OpenAlex · Extracted main text
We study instrumental variable regression (IVaR) under differential privacy constraints. Classical IVaR methods (like two-stage least squares regression) rely on solving moment equations that directly use sensitive covariates and instruments, creating significant risks of privacy leakage and posing challenges in designing algorithms that are both statistically efficient and differentially private. We propose a noisy two-state gradient descent algorithm that ensures $\rho$-zero-concentrated differential privacy by injecting carefully calibrated noise into the gradient updates. Our analysis establishes finite-sample convergence rates for the proposed method, showing that the algorithm achieves consistency while preserving privacy. In particular, we derive precise bounds quantifying the trade-off among privacy parameters, sample size, and iteration-complexity. To the best of our knowledge, this is the first work to provide both privacy guarantees and provable convergence rates for instrumental variable regression in linear models. We further validate our theoretical findings with experiments on both synthetic and real datasets, demonstrating that our method offers practical accuracy-privacy trade-offs.
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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 | Angrist, Joshua D. and Krueger, Alan B (2001) Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments | 0.737 | 3 | 2 | 100% |
| 2 | Bun, Mark and Steinke, Thomas (2016) Concentrated differential privacy: Simplifications, extensions, and lower bounds | 0.737 | 3 | 2 | 100% |
| 3 | Dwork, Cynthia and McSherry, Frank and Nissim, Kobbi and Smith, Adam (2006) Calibrating noise to sensitivity in private data analysis | 0.644 | 2 | 2 | 100% |
| 4 | Bassily, Raef and Smith, Adam and Thakurta, Abhradeep (2014) Private empirical risk minimization: Efficient algorithms and tight error bounds | 0.585 | 3 | 1 | 100% |
| 5 | Tsfadia, Eliad and Cohen, Edith and Kaplan, Haim and Mansour, Yishay… (2022) Friendlycore: Practical differentially private aggregation | 0.511 | 4 | 2 | 25% |
| 6 | Vershynin, Roman (2018) High-Dimensional Probability: An Introduction with Applications in Data Science | 0.511 | 2 | 2 | 50% |
| 7 | Abadi, Martin and Chu, Andy and Goodfellow, Ian and McMahan, H Brend… (2016) Deep learning with differential privacy | 0.511 | 2 | 1 | 100% |
| 8 | Sheffet, Or (2017) Differentially private ordinary least squares | 0.511 | 2 | 1 | 100% |
| 9 | Wang, Yu-Xiang and Balle, Borja and Kasiviswanathan, Shiva Prasad (2019) Subsampled rényi differential privacy and analytical moments accountant | 0.511 | 2 | 1 | 100% |
| 10 | Westoff, Charles F. and Parke, Robert (1972) Demographic and social aspects of population growth | 0.405 | 1 | 1 | 100% |
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