Related papers: A new Nested Cross Approximation

Hyperdimensional Computing (HDC), also known as Vector-Symbolic Architectures (VSA), is a promising framework for the development of cognitive architectures and artificial intelligence systems, as well as for technical applications and…

Vehicle Routing Problems (VRPs) are significant Combinatorial Optimization (CO) problems holding substantial practical importance. Recently, Neural Combinatorial Optimization (NCO), which involves training deep learning models on extensive…

This paper presents an efficient method to perform Structured Matrix Approximation by Separation and Hierarchy (SMASH), when the original dense matrix is associated with a kernel function. Given points in a domain, a tree structure is first…

The introduction of Neural Quantum States (NQS) has recently given a new twist to variational Monte Carlo (VMC). The ability to systematically reduce the bias of the wave function ansatz renders the approach widely applicable. However,…

Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…

Qualitative Comparative Analysis (QCA) has been increasingly used in recent years due to its purported construction of a middle path between case-oriented and variable-oriented methods. Despite its popularity, a key element of the method…

Capsules are the name given by Geoffrey Hinton to vector-valued neurons. Neural networks traditionally produce a scalar value for an activated neuron. Capsules, on the other hand, produce a vector of values, which Hinton argues correspond…

Simulation of high-order nonlinear system requires extensive computational resources, especially in modern VLSI backend design where bifurcation-induced instability and chaos-like transient behaviors pose challenges. We present S-Crescendo…

Neural network-based variational Monte Carlo (NN-VMC) has emerged as a promising cutting-edge technique of ab initio quantum chemistry. However, the high computational cost of existing approaches hinders their applications in realistic…

In Software Product Line Engineering (SPLE) families of systems are designed, rather than developing the individual systems independently. Combinatorial Interaction Testing has proven to be effective for testing in the context of SPLE,…

We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations. The new algorithm uses Green's representation formula in…

The challenges involved in executing neural networks (NNs) at the edge include providing diversity, flexibility, and sustainability. That implies, for instance, supporting evolving applications and algorithms energy-efficiently. Using…

Nonnegative matrix factorization (NMF) is a widely used linear dimensionality reduction technique for nonnegative data. NMF requires that each data point is approximated by a convex combination of basis elements. Archetypal analysis (AA),…

When performing Bayesian inference using Sequential Monte Carlo (SMC) methods, two considerations arise: the accuracy of the posterior approximation and computational efficiency. To address computational demands, Sequential Monte Carlo…

We present a method for calculating the full counting statistics of a nonequilibrium quantum system based on the propagator noncrossing approximation (NCA). This numerically inexpensive method can provide higher order cumulants for extended…

A PCA based sequence-to-vector (seq2vec) dimension reduction method for the text classification problem, called the tree-structured multi-stage principal component analysis (TMPCA) is presented in this paper. Theoretical analysis and…

Diagnosis of hematological malignancies depends on accurate identification of white blood cells in peripheral blood smears. Deep learning techniques are emerging as a viable solution to scale and optimize this process by automatic cell…

Large kernel systems are prone to be ill-conditioned. Pivoted Cholesky decomposition (PCD) render a stable and efficient solution to the systems without a perturbation of regularization. This paper proposes a new PCD algorithm by tuning…

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…

Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the Streaming Tensor Train Approximation (STTA), a new class of algorithms for approximating a given tensor…