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Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…
The article considers minimization of the expectation of convex function. Problems of this type often arise in machine learning and a number of other applications. In practice, stochastic gradient descent (SGD) and similar procedures are…
The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for…
Low-rank matrix approximation plays an important role in various applications such as image processing, signal processing and data analysis. The existing methods require a guess of the ranks of matrices that represent images or involve…
Compact optimization algorithms are a class of Estimation of Distribution Algorithms (EDAs) characterized by extremely limited memory requirements (hence they are called "compact"). As all EDAs, compact algorithms build and update a…
Variational Autoencoders and their many variants have displayed impressive ability to perform dimensionality reduction, often achieving state-of-the-art performance. Many current methods however, struggle to learn good representations in…
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…
This paper studies a low-communication algorithm for solving elliptic partial differential equations (PDE's) on high-performance machines, the nested iteration with range decomposition algorithm (NIRD). Previous work has shown that NIRD…
This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality…
This paper investigates the eigenvalue computation problem of the dual quaternion Hermitian matrix closely related to multi-agent group control. Recently, power method was proposed by Cui and Qi in Journal of Scientific Computing, 100…
Recent years have witnessed the great success of vision transformer (ViT), which has achieved state-of-the-art performance on multiple computer vision benchmarks. However, ViT models suffer from vast amounts of parameters and high…
CUR matrix decomposition is a randomized algorithm that can efficiently compute the low rank approximation for a given rectangle matrix. One limitation with the existing CUR algorithms is that they require an access to the full matrix A for…
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…
CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for…
Image compression is a widely used technique to reduce the spatial redundancy in images. Recently, learning based image compression has achieved significant progress by using the powerful representation ability from neural networks.…
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…
For many hard computational problems, simple algorithms that run in time $2^n \cdot n^{O(1)}$ arise, say, from enumerating all subsets of a size-$n$ set. Finding (exponentially) faster algorithms is a natural goal that has driven much of…
To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown…
Image compression and reconstruction are crucial for various digital applications. While contemporary neural compression methods achieve impressive compression rates, the adoption of such technology has been largely hindered by the…
Partitioning a graph into blocks of roughly equal weight while cutting only few edges is a fundamental problem in computer science with numerous practical applications. While shared-memory parallel partitioners have recently matured to…