Related papers: Parametric Hierarchical Matrix Approximations to K…

With near-term quantum devices available and the race for fault-tolerant quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum…

Hierarchical Topic Models (HTMs) are useful for discovering topic hierarchies in a collection of documents. However, traditional HTMs often produce hierarchies where lowerlevel topics are unrelated and not specific enough to their…

A new method for hierarchical clustering is presented. It combines treelets, a particular multiscale decomposition of data, with a projection on a reproducing kernel Hilbert space. The proposed approach, called kernel treelets (KT),…

This paper introduces a hierarchical framework to incorporate Hellinger distance methods into Bayesian analysis. We propose to modify a prior over non-parametric densities with the exponential of twice the Hellinger distance between a…

Artificial intelligence (AI) application domains consist of a mix of tensor operations with high and low arithmetic intensities (aka reuse). Hierarchical (i.e. compute along multiple levels of memory hierarchy) and heterogeneous (multiple…

In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…

We describe a randomized algorithm for producing a near-optimal hierarchical off-diagonal low-rank (HODLR) approximation to an $n\times n$ matrix $\mathbf{A}$, accessible only though matrix-vector products with $\mathbf{A}$ and…

Kernel-based clustering algorithms have the ability to capture the non-linear structure in real world data. Among various kernel-based clustering algorithms, kernel k-means has gained popularity due to its simple iterative nature and ease…

The graph partitioning problem has many applications in scientific computing such as computer aided design, data mining, image compression and other applications with sparse-matrix vector multiplications as a kernel operation. In many cases…

We present a novel characterization of the mapping of multiple parallelism forms (e.g. data and model parallelism) onto hierarchical accelerator systems that is hierarchy-aware and greatly reduces the space of software-to-hardware mapping.…

With the rapid development of digital information, the data volume generated by humans and machines is growing exponentially. Along with this trend, machine learning algorithms have been formed and evolved continuously to discover new…

Traditionally, classifying large hierarchical labels with more than 10000 distinct traces can only be achieved with flatten labels. Although flatten labels is feasible, it misses the hierarchical information in the labels. Hierarchical…

Quantum machine learning with quantum kernels for classification problems is a growing area of research. Recently, quantum kernel alignment techniques that parameterise the kernel have been developed, allowing the kernel to be trained and…

In this paper, we develop a quadrature framework for large-scale kernel machines via a numerical integration representation. Considering that the integration domain and measure of typical kernels, e.g., Gaussian kernels, arc-cosine kernels,…

Hashing method maps similar data to binary hashcodes with smaller hamming distance, and it has received a broad attention due to its low storage cost and fast retrieval speed. However, the existing limitations make the present algorithms…

Support vector machines and kernel methods have recently gained considerable attention in chemoinformatics. They offer generally good performance for problems of supervised classification or regression, and provide a flexible and…

This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…

The computational complexity of kernel methods has often been a major barrier for applying them to large-scale learning problems. We argue that this barrier can be effectively overcome. In particular, we develop methods to scale up kernel…

Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However,…

Hierarchical matrix approximations have gained significant traction in the machine learning and scientific community as they exploit available low-rank structures in kernel methods to compress the kernel matrix. The resulting compressed…