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.
Private algorithms approximate matrices with private data.
problem Approximate matrices with same spectrum using private data.
method Differential privacy algorithms for unitary orbit optimization.
result Upper and lower bounds on approximation error.
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…
UPCA solves data matrix completion with permuted columns.
problem Data matrix completion with permuted columns.
method Algebraic geometry and two-stage algorithm.
result UPCA recovers the ground-truth matrix from corrupted data.
Efficient private matrix analysis algorithms for recent variants.
problem Private analysis of recent matrix updates.
method Identifying sufficient conditions on positive semidefinite matrices.
result First efficient differentially private algorithms for various matrix analysis tasks.
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.
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.
In many signal processing and machine learning applications, datasets containing private information are held at different locations, requiring the development of distributed privacy-preserving algorithms. Tensor and matrix factorizations are key components of many processing pipelines. In the distributed setting, diff…
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.
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.
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.
JME continually estimates data moments privately and accurately.
problem Private and accurate continual estimation of data moments.
method Uses matrix mechanism and joint sensitivity analysis.
result Improves accuracy in estimating mean and covariance with reduced noise.
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.
We propose a new input perturbation mechanism for publishing a covariance matrix to achieve (ε,0)-differential privacy. Our mechanism uses a Wishart distribution to generate matrix noise. In particular, We apply this mechanism to principal component analysis. Our mechanism is able to keep the positive semi-definitene…
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.
Study on InstaHide's security, linking to phase retrieval problem.
problem Security of InstaHide scheme for private dataset sharing.
method Design of a provable algorithm for private vector recovery.
result Private vectors can be recovered using synthetic vectors and public vectors.
Enhances DP linear regression using public data moments.
problem Limited utility of traditional DP methods in linear regression.
method Transform private data using public second-moment matrix for a better OLSE.
result Improved accuracy and robustness of OLSE in DP linear regression.
Privacy affects how much data is needed for CVaR optimization.
problem Privacy constraints impact the effective sample size for CVaR optimization.
method Analyzes the privacy-relevant sample size and decomposes CVaR excess risk.
result The effective private tail sample size is εnτ, affecting CVaR learning rates.
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.
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.
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.
We propose a privacy-enhanced matrix factorization recommender that exploits the fact that users can often be grouped together by interest. This allows a form of "hiding in the crowd" privacy. We introduce a novel matrix factorization approach suited to making recommendations in a shared group (or nym) setting and the …
PMT uses public data moments to make DP feasible for unbounded data.
problem Applying differential privacy to unbounded data distributions.
method Public-moment-guided Truncation (PMT) using second-moments from public data.
result PMT improves the accuracy and stability of DP models.
A new scheme for private computation splits client data into shares for server operations.
problem Private computation between client and server without revealing data.
method Stochastic scheme splitting client data into privatized shares.
result Server performs operations on privatized shares without learning raw data.
Federated approach protects privacy while learning user patterns.
problem Protecting sensitive data in recommendation systems.
method Differentially private prototypes for global and local models.
result Local adaptation improves recommendation accuracy and relevance.
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.
Unified framework for nonconvex matrix completion with linearly parameterized factors.
problem Matrix completion with improved accuracy using linearly parameterized factors.
method Unified nonconvex optimization framework with Correlated Parametric Factorization condition.
result Uniform upper bounds for low-rank estimation at any local minimum.
We compare the sample complexity of private learning [Kasiviswanathan et al. 2008] and sanitization~[Blum et al. 2008] under pure ε-differential privacy [Dwork et al. TCC 2006] and approximate (ε,δ)-differential privacy [Dwork et al. Eurocrypt 2006]. We show that the sample complexity of these tasks under approxima…
Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume that the input partially-observed matrix is low rank. The success of these methods…
New DP mechanisms improve ML privacy-utility-computational tradeoffs.
problem Improving privacy in machine learning with multiple passes over data.
method Formalized DP for adaptive streams, extended matrix factorization techniques, Fourier-transform-based mechanism.
result Substantial improvements in privacy-utility-computational tradeoffs over previous methods.
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 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.
A very simple interpretation of matrix completion problem is introduced based on statistical models. Combined with the well-known results from missing data analysis, such interpretation indicates that matrix completion is still a valid and principled estimation procedure even without the missing completely at random (M…
Recommender systems are widely used to recommend the most appealing items to users. These recommendations can be generated by applying collaborative filtering methods. The low-rank matrix completion method is the state-of-the-art collaborative filtering method. In this work, we show that the skewed distribution of rati…
Matrix completion is often applied to data with entries missing not at random (MNAR). For example, consider a recommendation system where users tend to only reveal ratings for items they like. In this case, a matrix completion method that relies on entries being revealed at uniformly sampled row and column indices can …
Study on markets with insiders receiving private signals affecting asset prices and information flow.
problem Understanding markets with heterogeneous information flows and private signals.
method Proves existence of a partial communication equilibrium with jumps in information and prices.
result The public information flow and asset prices jump at each private signal time, creating incomplete markets between jumps.
New method corrects bias in missing data for matrix completion.
problem Missing data bias in matrix completion.
method Causal model and synthetic nearest neighbors (SNN) method.
result Synthetic nearest neighbors (SNN) method provides consistent and normal estimates.
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion methods often assume a simple uniform missing mechanism. In this work, we study ma…
Study improves fractional posterior for 1-bit matrix completion.
problem Estimating a binary matrix from observed entries.
method Fractional posterior approach with low-rank factorization and spectral scaled Student priors.
result Concentration results for fractional posterior, demonstrating effectiveness in matrix recovery.
Paper develops new patterns for unique matrix completions.
problem Developing unique completions for non-random matrix patterns.
method Formulated low-rank matrix completion using Plucker coordinates.
result Provides two families of patterns for any rank.
A new framework for private Bayesian tests maintains interpretability and computational efficiency.
problem Lack of interpretability and inability to quantify evidence in confidential data.
method Differentially private Bayesian tests based on test statistics.
result Established results on Bayes factor consistency under the proposed framework.
A new method for 1-bit matrix completion that is faster and more accurate.
problem Estimating a low-rank matrix from binary observations.
method Majorization-Minimization Gauss-Newton (MMGN) method.
result MMGN outperforms existing methods in accuracy and speed.
We consider the problem of matrix completion with side information (\textit{inductive matrix completion}). In real-world applications many side-channel features are typically non-informative making feature selection an important part of the problem. We incorporate feature selection into inductive matrix completion by p…
Study shows how fast a specific matrix completion method works.
problem Completing a rank-one matrix from a subset of revealed entries.
method Alternating minimization approach for matrix completion.
result Polynomial upper bound on convergence rate.
Revealed preference theory studies the possibility of modeling an agent's revealed preferences and the construction of a consistent utility function. However, modeling agent's choices over preference orderings is not always practical and demands strong assumptions on human rationality and data-acquisition abilities. Th…
Proposes a transductive matrix completion method with calibration for multi-task learning.
problem Improving multi-task learning with multiple related data sources.
method Transductive matrix completion with calibration constraint.
result The proposed algorithm recovers incomplete feature and target matrices with improved results.