相关论文: Leverage Score Sampling for Tensor Product Matrice…

Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to…

In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational…

Generative models typically sample outputs independently, and recent inference-time guidance and scaling algorithms focus on improving the quality of individual samples. However, in real-world applications, users are often presented with a…

Recovery of sparse vectors and low-rank matrices from a small number of linear measurements is well-known to be possible under various model assumptions on the measurements. The key requirement on the measurement matrices is typically the…

The training process of neural networks is known to be time-consuming, and having a deep architecture only aggravates the issue. This process consists mostly of matrix operations, among which matrix multiplication is the bottleneck. Several…

This paper proposes methods for likelihood-based inference in multivariate linear regressions when the correlation matrix of the responses is separable; that is, it has a Kronecker product structure, but the variances are unrestricted. The…

Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large…

A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The…

We study the problem of estimating the optimal Q-function of $\gamma$-discounted Markov decision processes (MDPs) under the synchronous setting, where independent samples for all state-action pairs are drawn from a generative model at each…

This work brings together two powerful concepts in Gaussian processes: the variational approach to sparse approximation and the spectral representation of Gaussian processes. This gives rise to an approximation that inherits the benefits of…

We study computational-statistical gaps for improper learning in sparse linear regression. More specifically, given $n$ samples from a $k$-sparse linear model in dimension $d$, we ask what is the minimum sample complexity to efficiently (in…

Leverage scores, loosely speaking, reflect the importance of the rows and columns of a matrix. Ideally, given the leverage scores of a rank-$r$ matrix $M\in\mathbb{R}^{n\times n}$, that matrix can be reliably completed from just…

Recently, tensor data (or multidimensional array) have been generated in many modern applications, such as functional magnetic resonance imaging (fMRI) in neuroscience and videos in video analysis. Many efforts are made in recent years to…

Simulating many-body quantum systems is a promising task for quantum computers. However, the depth of most algorithms, such as product formulas, scales with the number of terms in the Hamiltonian, and can therefore be challenging to…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

The Neural Tangent Kernel (NTK) characterizes the behavior of infinitely wide neural nets trained under least squares loss by gradient descent. However, despite its importance, the super-quadratic runtime of kernel methods limits the use of…

Sparse general matrix multiplication (SpGEMM) is a fundamental building block in numerous scientific applications. One critical task of SpGEMM is to compute or predict the structure of the output matrix (i.e., the number of nonzero elements…

This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes…

In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…

Multi-output Gaussian process regression has become an important tool in uncertainty quantification, for building emulators of computationally expensive simulators, and other areas such as multi-task machine learning. We present a holistic…