Related papers: Robust Partially-Compressed Least-Squares
Embeddings play a pivotal role across various disciplines, offering compact representations of complex data structures. Randomized methods like Johnson-Lindenstrauss (JL) provide state-of-the-art and essentially unimprovable theoretical…
With massive high-dimensional data now commonplace in research and industry, there is a strong and growing demand for more scalable computational techniques for data analysis and knowledge discovery. Key to turning these data into knowledge…
Non-negative least squares (NNLS) problem is one of the most important fundamental problems in numeric analysis. It has been widely used in scientific computation and data modeling. In big data, the limitations of algorithm speed and…
This paper explores the challenges of PAC learning in semi-enclosed environments that face persistent disruptive noise and demonstrates the weaknesses of traditional learning models based on noise-free data. We present a novel algorithm…
Randomized regularized Kaczmarz algorithms have recently been proposed to solve tensor recovery models with {\it consistent} linear measurements. In this work, we propose a novel algorithm based on the randomized extended Kaczmarz algorithm…
Deep Neural Networks have achieved remarkable success relying on the developing availability of GPUs and large-scale datasets with increasing network depth and width. However, due to the expensive computation and intensive memory,…
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…
Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable…
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…
The random feature method (RFM), a mesh-free machine learning-based framework, has emerged as a promising alternative for solving PDEs on complex domains. However, for large three-dimensional nonlinear problems, attaining high accuracy…
In this paper, we propose a low-rank representation with symmetric constraint (LRRSC) method for robust subspace clustering. Given a collection of data points approximately drawn from multiple subspaces, the proposed technique can…
We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has…
When considering a model architecture, there are several ways to reduce its memory footprint. Historically, popular approaches included selecting smaller architectures and creating sparse networks through pruning. More recently, randomized…
We consider a least absolute deviation (LAD) approach to the robust phase retrieval problem that aims to recover a signal from its absolute measurements corrupted with sparse noise. To solve the resulting non-convex optimization problem, we…
This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard l1 -minimization algorithm, originally proposed in the context…
This work develops a robust diffusion recursive least squares algorithm to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. This algorithm minimizes an exponentially weighted…
In this article, we present a method for increasing adaptivity of an existing robust estimation algorithm by learning two parameters to better fit the residual distribution. The analyzed method uses these two parameters to calculate weights…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
Robust low-rank approximation under row-wise adversarial corruption can be achieved with a single pass, randomized procedure that detects and removes outlier rows by thresholding their projected norms. We propose a scalable, non-iterative…
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…