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Award ID contains: 1954233

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  1. ; ; ; (, Combinatorics, Probability and Computing)
    Free, publicly-accessible full text available July 1, 2026
  2. ; ; (, Proceedings of the American Mathematical Society)
    We show how randomized rounding based on Grothendieck’s identity can be used to prove a nearly tight bound on the covariance loss–the amount of covariance that is lost by taking conditional expectation. This result yields a new type of weak Szemeredi regularity lemma for positive semidefinite matrices and kernels. Moreover, it can be used to construct differentially private synthetic data. 
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    Free, publicly-accessible full text available February 1, 2026
  3. ; ; ; (, Information and Inference: A Journal of the IMA)
    Differentially private synthetic data provide a powerful mechanism to enable data analysis while protecting sensitive information about individuals. However, when the data lie in a high-dimensional space, the accuracy of the synthetic data suffers from the curse of dimensionality. In this paper, we propose a differentially private algorithm to generate low-dimensional synthetic data efficiently from a high-dimensional dataset with a utility guarantee with respect to the Wasserstein distance. A key step of our algorithm is a private principal component analysis (PCA) procedure with a near-optimal accuracy bound that circumvents the curse of dimensionality. Unlike the standard perturbation analysis, our analysis of private PCA works without assuming the spectral gap for the covariance matrix. 
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    Free, publicly-accessible full text available January 15, 2026
  4. ; ; (, Probability theory and related fields)
    Accepted Manuscript Full Text Available
  5. ; ; (, Foundations of Computational Mathematics)
    Accepted Manuscript Full Text Available
  6. ; ; (, 36th Annual Conference on Learning Theory)
    We present a highly effective algorithmic approach for generating ε-differentially private synthetic data in a bounded metric space with near-optimal utility guarantees under the 1-Wasserstein distance. 
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    Accepted Manuscript Full Text Available
  7. ; (, Artificial Intelligence)
    Full Text Available 
  8. ; ; (, IEEE Transactions on Information Theory)
    Accepted Manuscript Full Text Available
  9. ; ; (, SIAM Journal on Mathematics of Data Science)
    Full Text Available 
  10. ; ; (, SIAM journal on mathematics of data science)
    Accepted Manuscript Full Text Available