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Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…
We consider fast kernel summations in high dimensions: given a large set of points in $d$ dimensions (with $d \gg 3$) and a pair-potential function (the {\em kernel} function), we compute a weighted sum of all pairwise kernel interactions…
The efficient compression of kernel matrices, for instance the off-diagonal blocks of discretized integral equations, is a crucial step in many algorithms. In this paper, we study the application of Skeletonized Interpolation to construct…
Ising machines are emerging as a new technology for solving various classes of computationally hard problems of practical importance, yet their limits on structured SAT workloads, representative of numerous real-world applications, remain…
To speed up Gaussian process inference, a number of fast kernel matrix-vector multiplication (MVM) approximation algorithms have been proposed over the years. In this paper, we establish an exact fast kernel MVM algorithm based on exact…
Kernel matrices (e.g. Gram or similarity matrices) are essential for many state-of-the-art approaches to classification, clustering, and dimensionality reduction. For large datasets, the cost of forming and factoring such kernel matrices…
Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…
Quantum-Kit is a graphical desktop application for quantum circuit simulations. Its powerful, memory-efficient computational engine enables large-scale simulations on a desktop. The ability to design hybrid circuits, with both quantum and…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…
Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
In recent years, hardware-accelerated neural networks have gained significant attention for edge computing applications. Among various hardware options, crossbar arrays, offer a promising avenue for efficient storage and manipulation of…
Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
To address the increasing computational demands of artificial intelligence (AI) and big data, compute-in-memory (CIM) integrates memory and processing units into the same physical location, reducing the time and energy overhead of the…
We propose a simple yet effective multiple kernel clustering algorithm, termed simple multiple kernel k-means (SimpleMKKM). It extends the widely used supervised kernel alignment criterion to multi-kernel clustering. Our criterion is given…
Kernel methods are powerful tools in statistical learning, but their cubic complexity in the sample size n limits their use on large-scale datasets. In this work, we introduce a scalable framework for kernel regression with O(n log n)…
A novel parallel hybrid quantum-classical algorithm for the solution of the quantum-chemical ground-state energy problem on gate-based quantum computers is presented. This approach is based on the reduced density-matrix functional theory…
The One Sided Crossing Minimization (OSCM) problem is an optimization problem in graph drawing that aims to minimize the number of edge crossings in bipartite graph layouts. It has practical applications in areas such as network…