Related papers: Fast QR updating methods for statistical applicati…
The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized…
Quadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure between main effects…
The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis. For matrices with many more rows than columns, so-called "tall-and-skinny matrices," there is a…
This article presents matrix backpropagation algorithms for the QR decomposition of matrices $A_{m, n}$, that are either square (m = n), wide (m < n), or deep (m > n), with rank $k = min(m, n)$. Furthermore, we derive novel matrix…
Interprocessor communication often dominates the runtime of large matrix computations. We present a parallel algorithm for computing QR decompositions whose bandwidth cost (communication volume) can be decreased at the cost of increasing…
The CUR decomposition is a technique for low-rank approximation that selects small subsets of the columns and rows of a given matrix to use as bases for its column and rowspaces. It has recently attracted much interest, as it has several…
Based on the column pivoted QR decomposition, we propose some randomized algorithms including pass-efficient ones for the generalized CUR decompositions of matrix pair and matrix triplet. Detailed error analyses of these algorithms are…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…
This paper addresses computational challenges in estimating Quantile Regression with Selection (QRS). The estimation of the parameters that model self-selection requires the estimation of the entire quantile process several times. Moreover,…
Recurrence quantification analysis (RQA) is a widely used tool for studying complex dynamical systems, but its standard implementation requires computationally expensive calculations of recurrence plots (RPs) and line length histograms.…
The QR Decomposition (QRD) of communication channel matrices is a fundamental prerequisite to several detection schemes in Multiple-Input Multiple-Output (MIMO) communication systems. Herein, the main feature of the QRD is to transform the…
Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and related low-rank approximation techniques. QR with Column Pivoting (QRCP) is usually…
Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…
We consider the problem of computing a QR (or QZ) decomposition of a real, dense, tall and very skinny matrix. That is, the number of columns is tiny compared to the number of rows, rendering most computations completely or partially…
Matrix decompositions in dual number representations have played an important role in fields such as kinematics and computer graphics in recent years. In this paper, we present a QR decomposition algorithm for dual number matrices,…
An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides…
The efficient and accurate QR decomposition for matrices with hierarchical low-rank structures, such as HODLR and hierarchical matrices, has been challenging. Existing structure-exploiting algorithms are prone to numerical instability as…
Kernel density estimation and kernel regression are powerful but computationally expensive techniques: a direct evaluation of kernel density estimates at $M$ evaluation points given $N$ input sample points requires a quadratic…
We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop…
Quantile regression is a powerful tool for robust and heterogeneous learning that has seen applications in a diverse range of applied areas. However, its broader application is often hindered by the substantial computational demands arising…