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In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…

A primary computational problem in kernel regression is solution of a dense linear system with the $N\times N$ kernel matrix. Because a direct solution has an O($N^3$) cost, iterative Krylov methods are often used with fast matrix-vector…

Large Language Models (LLMs) present significant deployment challenges due to their immense size and computational requirements. Model compression techniques are essential for making these models practical for resource-constrained…

In many problems of supervised tensor learning (STL), real world data such as face images or MRI scans are naturally represented as matrices, which are also called as second order tensors. Most existing classifiers based on tensor…

We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…

Exploring the relationship among multiple sets of data from one same group enables practitioners to make better decisions in medical science and engineering. In this paper, we propose a sparse collaborative learning (SCL) model, an…

The prediction of spectral properties via linear response (LR) theory is an important tool in quantum chemistry for understanding photo-induced processes in molecular systems. With the advances of quantum computing, we recently adapted this…

In this paper we introduce a new method which employs the concept of "Orientation Vectors" to train a feed forward neural network and suitable for problems where large dimensions are involved and the clusters are characteristically sparse.…

Quantum computing enables the efficient resolution of complex problems, often outperforming classical methods across various applications. In 2009, Harrow, Hassidim and Lloyd proposed an algorithm for solving linear systems of equations,…

The rapid scaling of large language models~(LLMs) has made inference efficiency a primary bottleneck in the practical deployment. To address this, semi-structured sparsity offers a promising solution by strategically retaining $N$ elements…

Kernel methods play an important role in machine learning applications due to their conceptual simplicity and superior performance on numerous machine learning tasks. Expressivity of a machine learning model, referring to the ability of the…

We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat\'ern correlations whose smoothness parameter $\nu$ is a half-integer. The proposed algorithm only requires $\mathcal{O}(\nu^3 n)$ operations…

Multiple Kernel Learning, or MKL, extends (kernelized) SVM by attempting to learn not only a classifier/regressor but also the best kernel for the training task, usually from a combination of existing kernel functions. Most MKL methods seek…

Quantum machine learning (QML) is a promising field that explores the applications of quantum computing to machine learning tasks. A significant hurdle in the advancement of quantum machine learning lies in the development of efficient and…

Clustered Low Rank (CLR) framework for block-sparse and block-low-rank tensor representation and computation is described. The CLR framework depends on 2 parameters that control precision: one controlling the CLR block rank truncation and…

Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM).…

In recent years, Convolutional Neural Networks (CNNs) have enabled ubiquitous image processing applications. As such, CNNs require fast runtime (forward propagation) to process high-resolution visual streams in real time. This is still a…

Logistic regression is a widely used statistical model to describe the relationship between a binary response variable and predictor variables in data sets. It is often used in machine learning to identify important predictor variables.…

Simultaneously solving multiple related learning tasks is beneficial under a variety of circumstances, but the prior knowledge necessary to correctly model task relationships is rarely available in practice. In this paper, we develop a…

Low-rank metric learning aims to learn better discrimination of data subject to low-rank constraints. It keeps the intrinsic low-rank structure of datasets and reduces the time cost and memory usage in metric learning. However, it is still…