Related papers: A Framework for Private Matrix Analysis
Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…
In the fields of control theory and machine learning, the dynamic low-rank approximation for large-scale matrices has received substantial attention. Considering large-scale semilinear stiff matrix differential equations, we propose…
Currently known methods for this task either employ the computationally intensive \emph{exponential mechanism} or require an access to the covariance matrix, and therefore fail to utilize potential sparsity of the data. The problem of…
We study the classical problem of community recovery in stochastic block models with a fixed number of communities, with a twist: We seek algorithms that are stable with respect to node-wise changes in the graph structure, formally defined…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
We design algorithms for fitting a high-dimensional statistical model to a large, sparse network without revealing sensitive information of individual members. Given a sparse input graph $G$, our algorithms output a…
We consider the task of privately obtaining prediction error guarantees in ordinary least-squares regression problems with Gaussian covariates (with unknown covariance structure). We provide the first sample-optimal polynomial time…
We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…
We develop a framework for efficiently transforming certain approximation algorithms into differentially-private variants, in a black-box manner. Specifically, our results focus on algorithms A that output an approximation to a function f…
We study a class of private learning problems in which the data is a join of private and public features. This is often the case in private personalization tasks such as recommendation or ad prediction, in which features related to…
Non-negative matrix factorization is a popular unsupervised machine learning algorithm for extracting meaningful features from data which are inherently non-negative. However, such data sets may often contain privacy-sensitive user data,…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
Estimating a covariance matrix and its associated principal components is a fundamental problem in contemporary statistics. While optimal estimation procedures have been developed with well-understood properties, the increasing demand for…
We provide an improved analysis of standard differentially private gradient descent for linear regression under the squared error loss. Under modest assumptions on the input, we characterize the distribution of the iterate at each time…
This paper studies the principal component (PC) method-based estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PC estimators of loadings, which comes from the…
Through the lens of information-theoretic reductions, we examine a reductions approach to fair optimization and learning where a black-box optimizer is used to learn a fair model for classification or regression. Quantifying the complexity,…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…
This paper proposes a probabilistic model of subspaces based on the probabilistic principal component analysis (PCA). Given a sample of vectors in the embedding space -- commonly known as a snapshot matrix -- this method uses quantities…
We study the problem of differentially private (DP) matrix completion under user-level privacy. We design a joint differentially private variant of the popular Alternating-Least-Squares (ALS) method that achieves: i) (nearly) optimal sample…