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1. A Framework for Private Matrix Analysis in Sliding Window Model

   Upadhyay, Jalaj; Upadhyay, Sarvagya (January 2021, Proceedings of Machine Learning Research)

   We perform a rigorous study of private matrix analysis when only the last 𝑊 updates to matrices are considered useful for analysis. We show the existing framework in the non-private setting is not robust to noise required for privacy. We then propose a framework robust to noise and use it to give first efficient 𝑜(𝑊) space differentially private algorithms for spectral approximation, principal component analysis (PCA), multi-response linear regression, sparse PCA, and non-negative PCA. Prior to our work, no such result was known for sparse and non-negative differentially private PCA even in the static data setting. We also give a lower bound to demonstrate the cost of privacy in the sliding window model. 

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2. Better Private Distribution Testing by Leveraging Unverified Auxiliary Data

   Aliakbarpour, Maryam; Burudgunte, Arnav; Canonne, Clement; Rubinfeld, Ronitt (June 2025, 38th Annual Conference on Learning Theory (COLT 2025))

   We extend the framework of augmented distribution testing (Aliakbarpour, Indyk, Rubinfeld, and Silwal, NeurIPS 2024) to the differentially private setting. This captures scenarios where a data ana- lyst must perform hypothesis testing tasks on sensitive data, but is able to leverage prior knowledge (public, but possibly erroneous or untrusted) about the data distribution. We design private algorithms in this augmented setting for three flagship distribution testing tasks, uniformity, identity, and closeness testing, whose sample complexity smoothly scales with the claimed quality of the auxiliary information. We complement our algorithms with information- theoretic lower bounds, showing that their sample complexity is optimal (up to logarithmic factors). Keywords: distribution testing, identity testing, closeness testing, differential privacy, learning- augmented algorithms 

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3. Private-RAG: Answering Multiple Queries with LLMs while Keeping Your Data Private

   Wu, Ruihan; Wang, Erchi; Zhang, Zhiyuang; Wang, Yu-Xiang (August 2026, Conference on Language Modeling (COLM 2026))

   Retrieval-augmented generation (RAG) enhances large language models (LLMs) by retrieving documents from an external corpus at inference time. When this corpus contains sensitive information, however, unprotected RAG systems are at risk of leaking private information. Prior work has introduced differential privacy (DP) guarantees for RAG, but only in single-query settings, which fall short of realistic usage. In this paper, we study the more practical multi-query setting and propose two DP-RAG algorithms. The first, MURAG, leverages an individual privacy filter so that the accumulated privacy loss only depends on how frequently each document is retrieved rather than the total number of queries. The second, MURAG-Ada, further improves utility by privately releasing query-specific thresholds, enabling more precise selection of relevant documents. Our experiments across multiple LLMs and datasets demonstrate that the proposed methods scale to hundreds of queries within a practical DP budget (ε ≈ 10), while preserving meaningful utility. 

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4. Utility Analysis of Horizontally Merged Multi-Party Synthetic Data with Differential Privacy

   https://doi.org/10.1109/ISNCC49221.2020.9297254  

   Su, Bingyue; Liu, Fang (December 2020, 2020 IEEE International Symposium on Networks, Computers and Communications (ISNCC))

   A large amount of data is often needed to train machine learning algorithms with confidence. One way to achieve the necessary data volume is to share and combine data from multiple parties. On the other hand, how to protect sensitive personal information during data sharing is always a challenge. We focus on data sharing when parties have overlapping attributes but non-overlapping individuals. One approach to achieve privacy protection is through sharing differentially private synthetic data. Each party generates synthetic data at its own preferred privacy budget, which is then released and horizontally merged across the parties. The total privacy cost for this approach is capped at the maximum individual budget employed by a party. We derive the mean squared error bounds for the parameter estimation in common regression analysis based on the merged sanitized data across parties. We identify through theoretical analysis the conditions under which the utility of sharing and merging sanitized data outweighs the perturbation introduced for satisfying differential privacy and surpasses that based on individual party data. The experiments suggest that sanitized HOMM data obtained at a practically reasonable small privacy cost can lead to smaller prediction and estimation errors than individual parties, demonstrating the benefits of data sharing while protecting privacy. 

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5. Manipulation Attacks in Local Differential Privacy

   https://doi.org/10.29012/jpc.754  

   Cheu, Albert; Smith, Adam; Ullman, Jonathan (February 2021, Journal of Privacy and Confidentiality)

   Local differential privacy is a widely studied restriction on distributed algorithms that collect aggregates about sensitive user data, and is now deployed in several large systems. We initiate a systematic study of a fundamental limitation of locally differentially private protocols: they are highly vulnerable to adversarial manipulation. While any algorithm can be manipulated by adversaries who lie about their inputs, we show that any noninteractive locally differentially private protocol can be manipulated to a much greater extent---when the privacy level is high, or the domain size is large, a small fraction of users in the protocol can completely obscure the distribution of the honest users' input. We also construct protocols that are optimally robust to manipulation for a variety of common tasks in local differential privacy. Finally, we give simple experiments validating our  theoretical results, and demonstrating that protocols that are optimal without manipulation can have dramatically different levels of robustness to manipulation. Our results suggest caution when deploying local differential privacy and reinforce the importance of efficient cryptographic  techniques for the distributed emulation of centrally differentially private mechanisms. 

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