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In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm…

Multi-criteria decision-making often requires finding a small representative set from the database. A recently proposed method is the regret minimization set (RMS) query. RMS returns a size $r$ subset $S$ of dataset $D$ that minimizes the…

Low-rank representation (LRR) is an effective method for subspace clustering and has found wide applications in computer vision and machine learning. The existing LRR solver is based on the alternating direction method (ADM). It suffers…

Many imaging science tasks can be modeled as a discrete linear inverse problem. Solving linear inverse problems is often challenging, with ill-conditioned operators and potentially non-unique solutions. Embedding prior knowledge, such as…

Tensor decomposition (TD) is essential for analyzing high-dimensional sparse data, yet its irregular computations and memory-access patterns pose major performance challenges on modern parallel processors. Prior works rely on…

In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for…

Matrix representations are a powerful tool for designing efficient algorithms for combinatorial optimization problems such as matching, and linear matroid intersection and parity. In this paper, we initiate the study of matrix…

We propose a prox-regular-type low-rank constrained nonconvex nonsmooth optimization model for Robust Low-Rank Matrix Recovery (RLRMR), i.e., estimate problem of low-rank matrix from an observed signal corrupted by outliers. For RLRMR, the…

LU-factorization of matrices is one of the fundamental algorithms of linear algebra. The widespread use of supercomputers with distributed memory requires a review of traditional algorithms, which were based on the common memory of a…

Low Rank Decomposition of matrix - splitting a large matrix into a product of two smaller matrix offers a means for compression that reduces the parameters of a model without sparsification, and hence delivering more speedup on modern…

By lifting the ReLU function into a higher dimensional space, we develop a smooth multi-convex formulation for training feed-forward deep neural networks (DNNs). This allows us to develop a block coordinate descent (BCD) training algorithm…

To improve the training efficiency of federated learning (FL), previous research has employed low-rank decomposition techniques to reduce communication overhead. In this paper, we seek to enhance the performance of these low-rank…

Dictionary Learning (DL) is one of the leading sparsity promoting techniques in the context of image classification, where the "dictionary" matrix D of images and the sparse matrix X are determined so as to represent a redundant image…

We propose a theoretical framework to analyze semi-supervised classification under the low density separation assumption in a high-dimensional regime. In particular, we introduce QLDS, a linear classification model, where the low density…

The low-rank matrix recovery problem seeks to reconstruct an unknown $n_1 \times n_2$ rank-$r$ matrix from $m$ linear measurements, where $m\ll n_1n_2$. This problem has been extensively studied over the past few decades, leading to a…

This work considers low-rank canonical polyadic decomposition (CPD) under a class of non-Euclidean loss functions that frequently arise in statistical machine learning and signal processing. These loss functions are often used for certain…

This paper introduces a deep reinforcement learning-based block coordinate descent (DRL-based BCD) algorithm to address the nonconvex weighted sum-rate maximization (WSRM) problem with a total power constraint. Firstly, we present an…

Tensors decompositions are a class of tools for analysing datasets of high dimensionality and variety in a natural manner, with the Canonical Polyadic Decomposition (CPD) being a main pillar. While the notion of CPD is closely intertwined…

It is shown that over-parameterized neural networks can achieve minimax optimal rates of convergence (up to logarithmic factors) for learning functions from certain smooth function classes, if the weights are suitably constrained or…

We study binary optimization problems of the form \( \min_{x\in\{-1,1\}^n} f(Ax-b) \) with possibly nonsmooth loss \(f\). Following the lifted rank-one semidefinite programming (SDP) approach\cite{qian2023matrix}, we develop a…