Related papers: Gaussian Process Models with Low-Rank Correlation …
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
This paper expands the analysis of randomized low-rank approximation beyond the Gaussian distribution to four classes of random matrices: (1) independent sub-Gaussian entries, (2) independent sub-Gaussian columns, (3) independent bounded…
Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes provide a powerful probabilistic kernel learning framework, which allows learning high quality nonparametric regression models via methods such as Gaussian process regression. Nevertheless, the learning phase of Gaussian…
Geometric optimisation algorithms are developed that efficiently find the nearest low-rank correlation matrix. We show, in numerical tests, that our methods compare favourably to the existing methods in the literature. The connection with…
In this study, we have developed an incremental machine learning (ML) method that efficiently obtains the optimal model when a small number of instances or features are added or removed. This problem holds practical importance in model…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…
We propose a clustering-based generalized low rank approximation method, which takes advantage of appealing features from both the generalized low rank approximation of matrices (GLRAM) and cluster analysis. It exploits a more general form…
The expressive power of a Gaussian process (GP) model comes at a cost of poor scalability in the data size. To improve its scalability, this paper presents a low-rank-cum-Markov approximation (LMA) of the GP model that is novel in…
CUR and low-rank approximations are among most fundamental subjects of numerical linear algebra, with a wide range of applications to a variety of highly important areas of modern computing, which range from the machine learning theory and…
The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to…
Fine-tuning has become a popular approach to adapting large foundational models to specific tasks. As the size of models and datasets grows, parameter-efficient fine-tuning techniques are increasingly important. One of the most widely used…
Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank…
Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal…
Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic…
Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework…
We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel's Mercer expansion. In particular, we…
We provide guarantees for approximate Gaussian Process (GP) regression resulting from two common low-rank kernel approximations: based on random Fourier features, and based on truncating the kernel's Mercer expansion. In particular, we…