# Differentially Private Truncation of Unbounded Data via Public Second Moments

arXiv: https://arxiv.org/abs/2602.22282 · HTML: https://mlsanity.com/paper/2602.22282/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 25 Feb 2026.

## Builds on (most cited first, 17 of 17)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Deep Learning with Gaussian Differential Privacy](https://mlsanity.com/paper/1911.11607/) (2019)
- [Revisiting Gradient Clipping: Stochastic bias and tight convergence guarantees](https://mlsanity.com/paper/2305.01588/) (2023)
- [Communication-efficient distributed SGD with Sketching](https://mlsanity.com/paper/1903.04488/) (2019)
- [Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain](https://mlsanity.com/paper/1803.02596/) (2018)
- [Public Data-Assisted Mirror Descent for Private Model Training](https://mlsanity.com/paper/2112.00193/) (2021)
- [Leveraging Public Data for Practical Private Query Release](https://mlsanity.com/paper/2102.08598/) (2021)
- [Differentially Private Ordinary Least Squares](https://mlsanity.com/paper/1507.02482/) (2015)
- [Private Estimation with Public Data](https://mlsanity.com/paper/2208.07984/) (2022)
- [Differentially private inference via noisy optimization](https://mlsanity.com/paper/2103.11003/) (2021)
- [Differentially Private Bayesian Linear Regression](https://mlsanity.com/paper/1910.13153/) (2019)
- [Learning from Mixtures of Private and Public Populations](https://mlsanity.com/paper/2008.00331/) (2020)
- [Privately Answering Classification Queries in the Agnostic PAC Model](https://mlsanity.com/paper/1907.13553/) (2019)
- [Faster Differentially Private Convex Optimization via Second-Order Methods](https://mlsanity.com/paper/2305.13209/) (2023)
- [Combining Public and Private Data](https://mlsanity.com/paper/2111.00115/) (2021)
- [Canonical Noise Distributions and Private Hypothesis Tests](https://mlsanity.com/paper/2108.04303/) (2021)
- [Distribution-Invariant Differential Privacy](https://mlsanity.com/paper/2111.05791/) (2021)

## Abstract (arXiv)

Data privacy is important in the AI era, and differential privacy (DP) is one of the golden solutions. However, DP is typically applicable only if data have a bounded underlying distribution. We address this limitation by leveraging second-moment information from a small amount of public data. We propose Public-moment-guided Truncation (PMT), which transforms private data using the public second-moment matrix and applies a principled truncation whose radius depends only on non-private quantities: data dimension and sample size. This transformation yields a well-conditioned second-moment matrix, enabling its inversion with a significantly strengthened ability to resist the DP noise. Furthermore, we demonstrate the applicability of PMT by using penalized and generalized linear regressions. Specifically, we design new loss functions and algorithms, ensuring that solutions in the transformed space can be mapped back to the original domain. We have established improvements in the models' DP estimation through theoretical error bounds, robustness guarantees, and convergence results, attributing the gains to the conditioning effect of PMT. Experiments on synthetic and real datasets confirm that PMT substantially improves the accuracy and stability of DP models.