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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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124247371494 · Jun 202019922001200920172026
48 results for private matrix approximation

New bounds for private matrix approximation using Gaussian noise and Dyson Brownian Motion.

problem Private approximation of symmetric matrices with Gaussian noise.
method Viewing Gaussian noise as Dyson Brownian Motion to track eigenvalue and eigenvector evolution.
result Improved bounds on Frobenius-distance utility for private matrix approximation.

PACE-GGM uses Gaussian mechanism for private covariance estimation.

problem Private estimation of covariance matrices in high dimensions.
method Data-adaptive selection of entries, Gaussian mechanism, maximum-entropy reconstruction.
result Consistent improvements in estimation error compared to Gaussian mechanism and baselines.

Private ALS method improves matrix completion with tighter rates and better privacy.

problem Differential privacy in matrix completion for user-level privacy.
method Joint differentially private ALS method with tighter sample complexity and privacy trade-offs.
result Achieves nearly optimal sample complexity and best privacy/utility trade-off.

In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample covariance matrix. Then we develop a differentially private graphical lasso estimator by…

2019-09-06abs ↗pdf ↗

New method stabilizes private LASSO for high-dimensional data with diverse covariate scales.

problem Privacy constraints and heterogeneity in covariate scales degrade LASSO stability and accuracy.
method Gram-based anisotropic objective perturbation to counteract covariate structure.
result Significantly improves convergence and statistical efficiency of private LASSO estimators.

New algorithms for community detection in graphs with privacy constraints.

problem Community recovery in stochastic block models with node-wise privacy.
method Spectral clustering with privacy mechanisms, including privatized PCA, convex optimization, and matrix estimation.
result Developed algorithms that are computable in polynomial-time and achieve consistent community estimation under node differential privacy.

We improve private training accuracy with learning rate schedules and matrix factorizations.

problem Private training with learning rate schedules and correlated noise.
method General upper and lower bounds for learning rate schedules, memory-efficient constructions, and schedule-aware factorizations.
result Schedule-aware factorizations improve accuracy in private training.

Three new oracle-efficient algorithms for private synthetic data release.

problem Constructing private synthetic data that preserves statistical query answers.
method Oracle-efficient algorithms using optimization oracles for differential privacy.
result Better accuracy in large workload and high privacy regime compared to state-of-the-art.

Novel privatization framework for high-dimensional variable selection with differential privacy.

problem High-dimensional controlled variable selection with rigorous FDR control under differential privacy constraints.
method Gaussian Johnson-Lindenstrauss Transformation for privatizing the knockoff matrix.
result The proposed private variable selection procedure maintains statistical power even under strict privacy budgets.

New method for private linear regression under privacy constraints, achieving optimal rates.

problem Statistical complexity of private linear regression under unknown, ill-conditioned covariates.
method Information-Weighted Regression method
result Optimal convergence rates for both central and local privacy models.

AdOBEst-LDP improves privacy-preserving frequency estimation for categorical data.

problem Estimating categorical distributions online while preserving privacy.
method AdOBEst-LDP uses adaptive randomized response mechanism to enhance future data utility.
result AdOBEst-LDP selects optimal subset for LDP mechanism with high probability.

Paper develops DP methods for low-rank matrix estimation with near-optimal performance.

problem Estimating a low-rank matrix under differential privacy constraints.
method Introduced computationally efficient DP-initialization and Riemannian optimization-based DP-RGrad algorithm.
result DP-RGrad achieves near-optimal convergence rate under weak differential privacy constraints.

Lower bounds on private estimation of Gaussian covariance matrices.

problem Private estimation of Gaussian covariance matrices under various parameter regimes.
method Stein-Haff identity and fingerprinting lemma extensions.
result Lower bounds match existing upper bounds in the widest known parameters.

We show that every approximately differentially private learning algorithm (possibly improper) for a class HH with Littlestone dimension~dd requires Ω(log(d))Ω\bigl(\log^*(d)\bigr) examples. As a corollary it follows that the class of thresholds over N\mathbb{N} can not be learned in a private manner; this resolves open qu…

2018-06-04abs ↗pdf ↗

New algorithm estimates Gaussian means and covariances efficiently and privately.

problem Estimating Gaussian parameters privately and efficiently.
method Differentially private preconditioner to transform arbitrary Gaussian samples.
result First polynomial-time, sample-efficient estimator for arbitrary Gaussian distributions.

Efficiently estimates private least squares with linear error growth.

problem Private estimation of ordinary least squares with bounded residuals and leverage.
method Scaled noise added to a stable nonprivate estimator of the regression vector.
result Near-optimal accuracy guarantee with linear error growth in dimension.

Differential privacy is a cryptographically-motivated definition of privacy which has gained significant attention over the past few years. Differentially private solutions enforce privacy by adding random noise to a function computed over the data, and the challenge in designing such algorithms is to control the added…

2012-06-27abs ↗pdf ↗

We present a private learner for halfspaces over an arbitrary finite domain XRdX\subset \mathbb{R}^d with sample complexity mathrmpoly(d,2logX)mathrm{poly}(d,2^{\log^*|X|}). The building block for this learner is a differentially private algorithm for locating an approximate center point of m>poly(d,2logX)m>\mathrm{poly}(d,2^{\log^*|X|}) points -- a…

2019-02-27abs ↗pdf ↗

Paper optimizes private PCA for covariance estimation in statistics.

problem Private estimation of covariance matrices and principal components.
method Developed differentially private estimators for spiked covariance model.
result Established minimax rates of convergence for principal components and covariance matrix estimation.

New method for privacy amplification without sampling for matrix factorization.

problem Privacy amplification for differentially private model training with matrix factorization.
method Sampling-free bounds based on Rényi divergence and conditional composition.
result Stronger privacy guarantees for small ε, applicable to various matrices.

We extend Kyle's model to include stochastic liquidity and multiple assets.

problem Modeling informed trading with stochastic liquidity and multiple assets.
method Developed a variational formulation and derived a matrix-valued martingale depth process.
result A linear-Gaussian equilibrium with stochastic matrix-valued price impact.

Paper proposes no-regret algorithms for private GP bandit optimization.

problem Private Gaussian process bandit optimization.
method Combines uniform kernel approximator with random perturbations for differentially private GP bandit algorithms.
result Provable no-regret algorithms for stationary kernel functions in two DP settings.

New lower bounds for private covariance estimation of Gaussian distributions are proven.

problem Proving tight lower bounds for private estimation tasks under differential privacy.
method Generalized fingerprinting method for exponential families and private Assouad method.
result Tight lower bounds for private covariance estimation in Frobenius and spectral norms.

Private classification and online prediction are shown to be equivalent.

problem Learning with differential privacy and online prediction equivalence.
method Introducing global stability and proving equivalence between online learnability and private PAC learnability.
result Every concept class with finite Littlestone dimension can be learned by a differentially-private algorithm.

Paper introduces data-dependent SSP for private linear and logistic regression.

problem Private linear and logistic regression with better performance.
method Data-dependent sufficient statistic perturbation (SSP) for linear and logistic regression.
result Data-dependent SSP outperforms state-of-the-art methods for linear and logistic regression.