Related papers: Independent Low-Rank Matrix Analysis Based on Para…
Independent component analysis (ICA) is the most popular method for blind source separation (BSS) with a diverse set of applications, such as biomedical signal processing, video and image analysis, and communications. Maximum likelihood…
Digital image inpainting is an interpolation problem, inferring the content in the missing (unknown) region to agree with the known region data such that the interpolated result fulfills some prior knowledge. Low-rank and nonlocal…
This paper considers the low-observability state estimation problem in power distribution networks and develops a decentralized state estimation algorithm leveraging the matrix completion methodology. Matrix completion has been shown to be…
Low-rank factorization is a popular model compression technique that minimizes the error $\delta$ between approximated and original weight matrices. Despite achieving performances close to the original models when $\delta$ is optimized, a…
Low-rank matrix factorizations are a class of linear models widely used in various fields such as machine learning, signal processing, and data analysis. These models approximate a matrix as the product of two smaller matrices, where the…
In this paper, we introduce a method for fine-tuning Large Language Models (LLMs), inspired by Multi-Task learning in a federated manner. Our approach leverages the structure of each client's model and enables a learning scheme that…
Low-Rank Adaptation (LoRA) offers a parameter-efficient paradigm for tuning large models. While recent spectral initialization methods improve convergence and performance over the naive "Noise & Zeros" scheme, their extra computational and…
In this work, we propose efficient algorithms for joint independent subspace analysis (JISA), an extension of independent component analysis that deals with parallel mixtures, where not all the components are independent. We derive an…
Fitting autoregressive moving average (ARMA) time series models requires model identification before parameter estimation. Model identification involves determining the order of the autoregressive and moving average components which is…
Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…
Evaluation of large language models (LLMs) is increasingly critical, yet standard benchmarking methods rely on average accuracy, overlooking both the inherent stochasticity of LLM outputs and the heterogeneity of benchmark items. Item…
Independent component analysis (ICA) is a powerful method for blind source separation based on the assumption that sources are statistically independent. Though ICA has proven useful and has been employed in many applications, complete…
We propose a new method of independent component analysis (ICA) in order to extract appropriate features from high-dimensional data. In general, matrix factorization methods including ICA have a problem regarding the interpretability of…
Independent component analysis is intended to recover the mutually independent components from their linear mixtures. This technique has been widely used in many fields, such as data analysis, signal processing, and machine learning. To…
In this work, the Parareal algorithm is applied to evolution problems that admit good low-rank approximations and for which the dynamical low-rank approximation (DLRA) can be used as time stepper. Many discrete integrators for DLRA have…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…
Matrix Factorization (MF) is a very popular method for recommendation systems. It assumes that the underneath rating matrix is low-rank. However, this assumption can be too restrictive to capture complex relationships and interactions among…
The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By…
The motivation of this work is to illustrate the efficiency of some often overlooked alternatives to deal with optimization problems in systems and control. In particular, we will consider a problem for which an iterative linear matrix…
Low-rank matrix approximation is a fundamental tool in data analysis for processing large datasets, reducing noise, and finding important signals. In this work, we present a novel truncated LU factorization called Spectrum-Revealing LU…