Related papers: Error Estimation for Sketched SVD via the Bootstra…
Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
Singular Value Decomposition (SVD) is a powerful tool in linear algebra.We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD…
The massive scale of pretrained models has made efficient compression essential for practical deployment. Low-rank decomposition based on the singular value decomposition (SVD) provides a principled approach for model reduction, but its…
The soft SVD is a robust matrix decomposition algorithm and a key component of matrix completion methods. However, computing the soft SVD for large sparse matrices is often impractical using conventional numerical methods for the SVD due to…
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…
Sketch-based modeling strives to bring the ease and immediacy of drawing to the 3D world. However, while drawings are easy for humans to create, they are very challenging for computers to interpret due to their sparsity and ambiguity. We…
Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral…
When machine learning models are trained continually on a sequence of tasks, they are often liable to forget what they learned on previous tasks--a phenomenon known as catastrophic forgetting. Proposed solutions to catastrophic forgetting…
This paper introduces two methods for verifying the singular values of the structured matrix denoted by $R^{-H}AR^{-1}$, where $R$ is a nonsingular matrix and $A$ is a general nonsingular square matrix. The first of the two methods uses the…
Visual similarities discovery (VSD) is an important task with broad e-commerce applications. Given an image of a certain object, the goal of VSD is to retrieve images of different objects with high perceptual visual similarity. Although…
The immense amount of daily generated and communicated data presents unique challenges in their processing. Clustering, the grouping of data without the presence of ground-truth labels, is an important tool for drawing inferences from data.…
Dealing with zero singular values can be quite challenging, as they have the potential to cause numerous numerical difficulties. This paper presents a method for computing the singular value decomposition (SVD) of a nonnegative bidiagonal…
The spectral decomposition of a real skew-symmetric matrix $A$ can be mathematically transformed into a specific structured singular value decomposition (SVD) of $A$. Based on such equivalence, a skew-symmetric Lanczos bidiagonalization…
We propose a multilevel stochastic approximation (MLSA) scheme for the computation of the value-at-risk (VaR) and expected shortfall (ES) of a financial loss, which can only be computed via simulations conditionally on the realisation of…
We propose a randomized first order optimization method--SEGA (SkEtched GrAdient method)-- which progressively throughout its iterations builds a variance-reduced estimate of the gradient from random linear measurements (sketches) of the…
Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…
Large-scale distributed training of neural networks is often limited by network bandwidth, wherein the communication time overwhelms the local computation time. Motivated by the success of sketching methods in sub-linear/streaming…
In sketched clustering, a dataset of $T$ samples is first sketched down to a vector of modest size, from which the centroids are subsequently extracted. Advantages include i) reduced storage complexity and ii) centroid extraction complexity…
In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data. Comprehensive…