Related papers: Back to Square Roots: An Optimal Bound on the Matr…

In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). Our inner/outer approximating algorithms generate a sequence of upper/lower…

We consider the least squares regression problem, penalized with a combination of the $\ell_{0}$ and squared $\ell_{2}$ penalty functions (a.k.a. $\ell_0 \ell_2$ regularization). Recent work shows that the resulting estimators are of key…

We study memory-efficient matrix factorization for differentially private counting under continual observation. While recent work by Henzinger and Upadhyay 2024 introduced a factorization method with reduced error based on group algebra,…

This paper proposes new methodologies for conducting practical differentially private (DP) estimation and inference in high-dimensional linear regression. We first introduce a DP Bayesian Information Criterion (DP-BIC) for selecting the…

In this work, we develop a new fast algorithm, spaQR -- sparsified QR, for solving large, sparse linear systems. The key to our approach is using low-rank approximations to sparsify the separators in a Nested Dissection based Householder QR…

We study privacy amplification for differentially private model training with matrix factorization under random allocation (also known as the balls-in-bins model). Recent work by Choquette-Choo et al. (2025) proposes a sampling-based Monte…

In downlink multiuser multiple-input multiple-output (MIMO) systems, block diagonalization (BD) is a practical linear precoding scheme which achieves the same degrees of freedom (DoF) as the optimal linear/nonlinear precoding schemes.…

The maximal biclique enumeration problem in bipartite graphs is fundamental and has numerous applications in E-commerce and transaction networks. Most existing studies adopt a branch-and-bound framework, which recursively expands a partial…

This study presents an efficient approach for incomplete data classification, where the entries of samples are missing or masked due to privacy preservation. To deal with these incomplete data, a new kernel function with asymmetric…

Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…

This note studies the worst-case recovery error of low-rank and bisparse matrices as a function of the number of one-bit measurements used to acquire them. First, by way of the concept of consistency width, precise estimates are given on…

We consider algorithms for going from a "full" matrix to a condensed "band bidiagonal" form using orthogonal transformations. We use the framework of "algorithms by tiles". Within this framework, we study: (i) the tiled bidiagonalization…

Matrix factor model is drawing growing attention for simultaneous two-way dimension reduction of well-structured matrix-valued observations. This paper focuses on robust statistical inference for matrix factor model in the ``diverging…

Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…

In this paper, we leverage over-parameterization to design regularization-free algorithms for the high-dimensional single index model and provide theoretical guarantees for the induced implicit regularization phenomenon. Specifically, we…

It remains an open problem to find the optimal configuration of phase shifts under the discrete constraint for intelligent reflecting surface (IRS) in polynomial time. The above problem is widely believed to be difficult because it is not…

We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…

Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…

We propose a novel distance-based regularization method for deep metric learning called Multi-level Distance Regularization (MDR). MDR explicitly disturbs a learning procedure by regularizing pairwise distances between embedding vectors…

It is well-known that the Burer-Monteiro (B-M) factorization approach can efficiently solve low-rank matrix optimization problems under the RIP condition. It is natural to ask whether B-M factorization-based methods can succeed on any…