Related papers: Fast and Accurate SVD-Type Updating in Streaming D…
Decentralized stochastic optimization methods have gained a lot of attention recently, mainly because of their cheap per iteration cost, data locality, and their communication-efficiency. In this paper we introduce a unified convergence…
In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…
Currently, matrix decomposition is one of the most widely used collaborative filtering algorithms by using factor decomposition to effectively deal with large-scale rating matrix. It mainly uses the interaction records between users and…
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…
In this paper we present an improved dqds algorithm for computing all the singular values of a bidiagonal matrix to high relative accuracy. There are two key contributions: a novel deflation strategy that improves the convergence for badly…
This work provides simple algorithms for multi-class (and multi-label) prediction in settings where both the number of examples n and the data dimension d are relatively large. These robust and parameter free algorithms are essentially…
In this paper, we study the low-complexity channel reconstruction methods for downlink precoding in massive multiple-Input multiple-Output (MIMO) systems. When the user is allocated less streams than the number of its antennas, the base…
While Convolutional Neural Networks (CNNs) excel at learning complex latent-space representations, their over-parameterization can lead to overfitting and reduced performance, particularly with limited data. This, alongside their high…
A novel approach is given to overcome the computational challenges of the full-matrix Adaptive Gradient algorithm (Full AdaGrad) in stochastic optimization. By developing a recursive method that estimates the inverse of the square root of…
This manuscript describes the randomized algorithm randUTV for computing a so called UTV factorization efficiently. Given a matrix $A$, the algorithm computes a factorization $A = UTV^{*}$, where $U$ and $V$ have orthonormal columns, and…
The randomized singular value decomposition (SVD) is a popular and effective algorithm for computing a near-best rank $k$ approximation of a matrix $A$ using matrix-vector products with standard Gaussian vectors. Here, we generalize the…
In this paper, we present a Rank Revealing Randomized Singular Value Decomposition (R3SVD) algorithm to incrementally construct a low-rank approximation of a potentially large matrix while adaptively estimating the appropriate rank that can…
We consider the task of updating a matrix function $f(A)$ when the matrix $A\in{\mathbb C}^{n \times n}$ is subject to a low-rank modification. In other words, we aim at approximating $f(A+D)-f(A)$ for a matrix $D$ of rank $k \ll n$. The…
Singular Value Decomposition (SVD) has recently seen a surge of interest as a simple yet powerful tool for large language models (LLMs) compression, with a growing number of works demonstrating 20-80% parameter reductions at minimal…
Recently, the technique of local updates is a powerful tool in centralized settings to improve communication efficiency via periodical communication. For decentralized settings, it is still unclear how to efficiently combine local updates…
The development of the manufacturing systems has made it increasingly necessary to monitor the data generated by multiple interconnected subsystems with rapid incoming of samples. Based on incremental Singular Value Decomposition (ISVD), we…
Given multiple time series data, how can we efficiently find latent patterns in an arbitrary time range? Singular value decomposition (SVD) is a crucial tool to discover hidden factors in multiple time series data, and has been used in many…
Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems. Some form of dimensionality reduction is required to make the problem tractable in general. In this paper, we propose…
Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…
This paper discusses a few algorithms for updating the approximate Singular Value Decomposition (SVD) in the context of information retrieval by Latent Semantic Indexing (LSI) methods. A unifying framework is considered which is based on…