Related papers: Fast Generalized Matrix Regression with Applicatio…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
This paper develops a new class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized sketching to accelerate subspace projection methods, such as GMRES and Rayleigh--Ritz. This approach…
Gaussian Mixture Models (GMMs) range among the most frequently used models in machine learning. However, training large, general GMMs becomes computationally prohibitive for datasets that have many data points $N$ of high-dimensionality…
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…
Generalized singular values (GSVs) play an essential role in the comparative analysis. In the real world data for comparative analysis, both data matrices are usually numerically low-rank. This paper proposes a randomized algorithm to first…
We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive…
Sketched gradient algorithms have been recently introduced for efficiently solving the large-scale constrained Least-squares regressions. In this paper we provide novel convergence analysis for the basic method {\it Gradient Projection…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
Although many techniques have been applied to matrix factorization (MF), they may not fully exploit the feature structure. In this paper, we incorporate the grouping effect into MF and propose a novel method called Robust Matrix…
The power method is one of the most fundamental tools for extracting top principal components from data through low-rank matrix approximation. Yet, when the target rank is large, the cost of matrix multiplication associated with this…
We present an approximate algorithm for matrix multiplication based on matrix sketching techniques. First one of the matrix is chosen and sparsified using the online matrix sketching algorithm, and then the matrix product is calculated…
Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
Matrix sketching is a recently developed data compression technique. An input matrix A is efficiently approximated with a smaller matrix B, so that B preserves most of the properties of A up to some guaranteed approximation ratio. In so…
With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…
In this paper we discuss an application of Stochastic Approximation to statistical estimation of high-dimensional sparse parameters. The proposed solution reduces to resolving a penalized stochastic optimization problem on each stage of a…
This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…
Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…
Graph Convolutional Networks (GCNs) are recently getting much attention in bioinformatics and chemoinformatics as a state-of-the-art machine learning approach with high accuracy. GCNs process convolutional operations along with graph…