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We study model personalization under user-level differential privacy (DP) in the shared representation framework. In this problem, there are $n$ users whose data is statistically heterogeneous, and their optimal parameters share an unknown…
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arithmetic, BMF employs the Boolean OR and AND operations for the…
Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices. Low-rank matrix approximation algorithms are widely used to address…
Matrix completion is one of the key problems in signal processing and machine learning. In recent years, deep-learning-based models have achieved state-of-the-art results in matrix completion. Nevertheless, they suffer from two drawbacks:…
We study continual mean estimation, where data vectors arrive sequentially and the goal is to maintain accurate estimates of the running mean. We address this problem under user-level differential privacy, which protects each user's entire…
We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…
Biclustering is an effective technique in data mining and pattern recognition. Biclustering algorithms based on traditional clustering face two fundamental limitations when processing high-dimensional data: (1) The distance concentration…
Differential privacy is a promising privacy-preserving paradigm for statistical query processing over sensitive data. It works by injecting random noise into each query result, such that it is provably hard for the adversary to infer the…
Sliced inverse regression (SIR, Li 1991) is a pioneering work and the most recognized method in sufficient dimension reduction. While promising progress has been made in theory and methods of high-dimensional SIR, two remaining challenges…
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…
Poisson subsampling is the default sampling scheme in differentially private machine learning, largely because its unstructured randomness yields tractable privacy amplification analyses. Yet this same randomness introduces substantial…
Matrix factorization is a popular framework for modeling low-rank data matrices. Motivated by manifold learning problems, this paper proposes a quadratic matrix factorization (QMF) framework to learn the curved manifold on which the dataset…
Many Bayesian statistical inference problems come down to computing a maximum a-posteriori (MAP) assignment of latent variables. Yet, standard methods for estimating the MAP assignment do not have a finite time guarantee that the algorithm…
Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined…
Sliced inverse regression (SIR) is a pioneer tool for supervised dimension reduction. It identifies the effective dimension reduction space, the subspace of significant factors with intrinsic lower dimensionality. In this paper, we propose…
We study the problem of constructing explicit families of matrices which cannot be expressed as a product of a few sparse matrices. In addition to being a natural mathematical question on its own, this problem appears in various…
We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of…
Electronic phased-array radars offer new possibilities for radar search pattern optimization by using bi-dimensional beam-forming and beam-steering. Radar search pattern optimization can be approximated as a set cover problem and solved…
In this paper, we study sparse factorization of the (scaled) square all-ones matrix $J$ of arbitrary order. We introduce the concept of hierarchically banded matrices and propose two types of hierarchically banded factorization of $J$: the…
Layer factorization has emerged as a widely used technique for training memory-efficient neural networks. However, layer factorization methods face several challenges, particularly a lack of robustness during the training process. To…