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ARXIV:2603.18254 · BAYESIAN ESTIMATION · SUBMITTED 02 APR · 02:30 UTC · FRESHNESS STALE
ARXIV:2603.18254BAYESIAN ESTIMATIONSUBMITTED 02 APR · 02:30 UTCFRESHNESS STALESitan Chen · Jingqiu Ding · Mahbod Majid · Walter McKelvie · arXiv
Develops efficient algorithms for differentially private Bayesian estimation with theoretical utility guarantees, addressing a gap in existing methods for Gaussian mean estimation and linear regression.
Opportunity summary
Pain Develops efficient algorithms for differentially private Bayesian estimation with theoretical utility guarantees, addressing a gap in existing methods for Gaussian mean estimation and linear regression.
Evidence 0 refs | 0 sources | 17% coverage
Blocker Evidence unverified
Develops efficient algorithms for differentially private Bayesian estimation with theoretical utility guarantees, addressing a gap in existing methods for Gaussian mean estimation and linear regression. Yet in many real-world use cases where these methods…
Bayesian methods lie at the heart of modern data science and provide a powerful scaffolding for estimation in data-constrained settings and principled quantification and propagation of uncertainty. Yet in many real-world use cases where…
ScienceToStartup currently rates this 3.0/10 on the public viability pass. In this work, we give the first efficient algorithms for both of these problems that achieve mean-squared error $(1+o(1))\mathrm{OPT}$ and additionally show that both…
Bayesian Estimation moved forward this cycle; last verified April 2026. Public score 3.0/10.
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Develops efficient algorithms for differentially private Bayesian estimation with theoretical utility guarantees, addressing a gap in existing methods for Gaussian mean estimation and linear regression.
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10.48550/arXiv.2603.18254Develops efficient algorithms for differentially private Bayesian estimation with theoretical utility guarantees, addressing a gap in existing methods for Gaussian mean estimation and linear regression.
Abstract
Bayesian methods lie at the heart of modern data science and provide a powerful scaffolding for estimation in data-constrained settings and principled quantification and propagation of uncertainty. Yet in many real-world use cases where these methods are deployed, there is a natural need to preserve the privacy of the individuals whose data is being scrutinized. While a number of works have attempted to approach the problem of differentially private Bayesian estimation through either reasoning about the inherent privacy of the posterior distribution or privatizing off-the-shelf Bayesian methods, these works generally do not come with rigorous utility guarantees beyond low-dimensional settings. In fact, even for the prototypical tasks of Gaussian mean estimation and linear regression, it was unknown how close one could get to the Bayes-optimal error with a private algorithm, even in the simplest case where the unknown parameter comes from a Gaussian prior. In this work, we give the first efficient algorithms for both of these problems that achieve mean-squared error $(1+o(1))\mathrm{OPT}$ and additionally show that both tasks exhibit an intriguing computational-statistical gap. For Bayesian mean estimation, we prove that the excess risk achieved by our method is optimal among all efficient algorithms within the low-degree framework, yet is provably worse than what is achievable by an exponential-time algorithm. For linear regression, we prove a qualitatively similar lower bound. Our algorithms draw upon the privacy-to-robustness framework of arXiv:2212.05015, but with the curious twist that to achieve private Bayes-optimal estimation, we need to design sum-of-squares-based robust estimators for inherently non-robust objects like the empirical mean and OLS estimator. Along the way we also add to the sum-of-squares toolkit a new kind of constraint based on short-flat decompositions.
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PROBLEM
Develops efficient algorithms for differentially private Bayesian estimation with theoretical utility guarantees, addressing a gap in existing methods for Gaussian mean estimation and linear regression. Yet in many real-world use cases where these methods are deployed, there is...
METHOD
Bayesian methods lie at the heart of modern data science and provide a powerful scaffolding for estimation in data-constrained settings and principled quantification and propagation of uncertainty. Yet in many real-world use cases where these methods are deployed, there is a nat...
RESULT
ScienceToStartup currently rates this 3.0/10 on the public viability pass. In this work, we give the first efficient algorithms for both of these problems that achieve mean-squared error $(1+o(1))\mathrm{OPT}$ and additionally show that both tasks exhibit an intriguing computati...
WHY NOW
Bayesian Estimation moved forward this cycle; last verified April 2026. Public score 3.0/10.
Abstract-backed public claims while anchored extraction refreshes.
Develops efficient algorithms for differentially private Bayesian estimation with theoretical utility guarantees, addressing a gap in existing methods for Gaussian mean estimation and linear regression. Yet in many real-world use cases where these methods are deployed, there is a natural need to preserve the privacy of the individuals whose data is being scrutinized.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Bayesian methods lie at the heart of modern data science and provide a powerful scaffolding for estimation in data-constrained settings and principled quantification and propagation of uncertainty. Yet in many real-world use cases where these methods are deployed, there is a natural need to preserve the privacy of the individuals whose data is being scrutinized.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
ScienceToStartup currently rates this 3.0/10 on the public viability pass. In this work, we give the first efficient algorithms for both of these problems that achieve mean-squared error $(1+o(1))\mathrm{OPT}$ and additionally show that both tasks exhibit an intriguing computational-statistical gap.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Bayesian Estimation moved forward this cycle; last verified April 2026. Public score 3.0/10.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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Develops efficient algorithms for differentially private Bayesian estimation with theoretical utility guarantees, addressing a gap in existing methods for Gaussian mean estimation and linear regression.
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Bayesian Estimation
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