相关论文: A hybrid DEIM and leverage scores based method for…

The singular value decomposition (SVD) is commonly used in applications requiring a low rank matrix approximation. However, the singular vectors cannot be interpreted in terms of the original data. For applications requiring this type of…

In this study we propose a-posteriori error estimation results to approximate the precision loss in quantities of interests computed using reduced order models. To generate the surrogate models we employ Proper Orthogonal Decomposition and…

We study algorithms for estimating the statistical leverage scores of rectangular dense or sparse matrices of arbitrary rank. Our approach is based on combining rank revealing methods with compositions of dense and sparse randomized…

We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be…

We derive a CUR-type factorization for tensors in the Tucker format based on interpolatory decomposition, which we will denote as Higher Order Interpolatory Decomposition (HOID). Given a tensor $\mathcal{X}$, the algorithm provides a set of…

Manifold learning techniques seek to discover structure-preserving mappings of high-dimensional data into low-dimensional spaces. While the new sets of coordinates specified by these mappings can closely parameterize the data, they are…

Sparse Discrete Empirical Interpolation Method (S-DEIM) was recently proposed for state estimation in dynamical systems when only a sparse subset of the state variables can be observed. The S-DEIM estimate involves a kernel vector whose…

High-dimensional dense embeddings have become central to modern Information Retrieval, but many dimensions are noisy or redundant. Recently proposed DIME (Dimension IMportance Estimation), provides query-dependent scores to identify…

Prior optimal CUR decomposition and near optimal column reconstruction methods have been established by combining BSS sampling and adaptive sampling. In this paper, we propose a new approach to the optimal CUR decomposition and near optimal…

The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized…

This paper introduces a novel approach to approximating continuous functions over high-dimensional hypercubes by integrating matrix CUR decomposition with hyperinterpolation techniques. Traditional Fourier-based hyperinterpolation methods…

Currently, public-key compression of supersingular isogeny Diffie-Hellman (SIDH) and its variant, supersingular isogeny key encapsulation (SIKE) involve pairing computation and discrete logarithm computation. In this paper, we propose novel…

We propose two approaches to estimate semiparametric discrete choice models for bundles. Our first approach is a kernel-weighted rank estimator based on a matching-based identification strategy. We establish its complete asymptotic…

We propose two approaches to estimate semiparametric discrete choice models for bundles. Our first approach is a kernel-weighted rank estimator based on a matching-based identification strategy. We establish its complete asymptotic…

Estimating mutual information between continuous random variables is often intractable and extremely challenging for high-dimensional data. Recent progress has leveraged neural networks to optimize variational lower bounds on mutual…

In this work, we introduce a novel methodology for divisive hierarchical clustering. Our divisive (``top-down'') approach is motivated by the fact that agglomerative hierarchical clustering (``bottom-up''), which is commonly used for…

We introduce a novel technique for constructing higher-order variational integrators for Hamiltonian systems of ODEs. In particular, we are concerned with generating globally smooth approximations to solutions of a Hamiltonian system. Our…

This paper proposes two new algorithms related to the Tucker tensor format. The first method is a new cross approximation for Tucker tensors, which we call Cross$^2$-DEIM. Cross$^2$-DEIM is an iterative method that uses a fiber sampling…

Dynamical low-rank approximation allows for solving large-scale matrix differential equations (MDEs) with significantly fewer degrees of freedom and has been applied to a growing number of applications. However, most existing techniques…

A Distributional (Single) Index Model (DIM) is a semi-parametric model for distributional regression, that is, estimation of conditional distributions given covariates. The method is a combination of classical single index models for the…