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Stein variational gradient descent (SVGD) and its variants have shown promising successes in approximate inference for complex distributions. In practice, we notice that the kernel used in SVGD-based methods has a decisive effect on the…

The cross-product matrix-based CJ-FEAST SVDsolver proposed previously by the authors is shown to compute the left singular vector possibly much less accurately than the right singular vector and may be numerically backward unstable when a…

Singular Value Decomposition (SVD) is a powerful tool for multivariate analysis. However, independent computation of the SVD for each sample taken from a bandlimited matrix random process will result in singular value sample paths whose…

Singular value decomposition (SVD) is one of the most popular compression methods that approximate a target matrix with smaller matrices. However, standard SVD treats the parameters within the matrix with equal importance, which is a simple…

With the advent of large language models (LLMs), numerous Post-Training Quantization (PTQ) strategies have been proposed to alleviate deployment barriers created by their enormous parameter counts. Quantization achieves compression by…

This chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data. We describe SVD methods for visualization of gene expression data, representation of the data using a…

The increasing number of applications requiring the solution of large scale singular value problems have rekindled interest in iterative methods for the SVD. Some promising recent ad- vances in large scale iterative methods are still…

Deploying large language models (LLMs) on mobile platforms faces significant challenges due to the limited memory and shared computational resources of the device. Resource availability may be an issue as it is directly impacted by the…

Standard rank-revealing factorizations such as the singular value decomposition and column pivoted QR factorization are challenging to implement efficiently on a GPU. A major difficulty in this regard is the inability of standard algorithms…

This thesis gives an overview of the state-of-the-art randomized linear algebra algorithms for singular value decomposition (SVD), including the presentation of existing pseudo-codes and theoretical error analysis. Our main focus is on…

Large language models (LLMs) have achieved remarkable success in natural language processing (NLP) tasks, yet their substantial memory requirements present significant challenges for deployment on resource-constrained devices. Singular…

Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern…

The traditional method of computing singular value decomposition (SVD) of a data matrix is based on a least squares principle, thus, is very sensitive to the presence of outliers. Hence the resulting inferences across different applications…

This paper proposes a versatile high-performance execution model, inspired by systolic arrays, for memory-bound regular kernels running on CUDA-enabled GPUs. We formulate a systolic model that shifts partial sums by CUDA warp primitives for…

We demonstrate a novel technique to obtain singular-value decomposition (SVD) of the coupled-cluster triple excitations amplitudes, $t_{ijk}^{abc}$. The presented method is based on the Golub-Kahan bidiagonalisation strategy and does not…

This paper describes the application of the code generated by the CAMPARY software to accelerate the solving of linear systems in the least squares sense on Graphics Processing Units (GPUs), in double double, quad double, and octo double…

Singular value decomposition (SVD) has a crucial role in model order reduction. It is often utilized in the offline stage to compute basis functions that project the high-dimensional nonlinear problem into a low-dimensionsl model which is,…

Emulating computationally intensive scientific simulations is crucial for enabling uncertainty quantification, optimization, and informed decision-making at scale. Gaussian Processes (GPs) offer a flexible and data-efficient foundation for…

Penalized quantile regression (QR) is widely used for studying the relationship between a response variable and a set of predictors under data heterogeneity in high-dimensional settings. Compared to penalized least squares, scalable…

Generative Recommendation (GR) reformulates recommendation as a next-token generation problem and has shown promise in industrial applications. However, extending GR to industrial advertising is non-trivial because the system must optimize…