相关论文: Fast Evaluation of Truncated Neumann Series by Low…

It is well known that kernel ridge regression (KRR) is a popular nonparametric regression estimator. Nonetheless, in the presence of a large data set with size $n\gg 1,$ the KRR estimator has the drawback to require an intensive…

Measurements on near-term quantum processors are inevitably subject to hardware imperfections that lead to readout errors. Mitigation of such unavoidable errors is crucial to better explore and extend the power of near-term quantum…

Kernel ridge regression (KRR) is a well-known and popular nonparametric regression approach with many desirable properties, including minimax rate-optimality in estimating functions that belong to common reproducing kernel Hilbert spaces…

In this paper, we propose a novel kernel stochastic gradient descent (SGD) algorithm for large-scale supervised learning with general losses. Compared to traditional kernel SGD, our algorithm improves efficiency and scalability through an…

Many real-world data are naturally represented as a sparse reorderable matrix, whose rows and columns can be arbitrarily ordered (e.g., the adjacency matrix of a bipartite graph). Storing a sparse matrix in conventional ways requires an…

We investigate the spectral properties of the product of $M$ complex non-Hermitian random matrices that are obtained by removing $L$ rows and columns of larger unitary random matrices uniformly distributed on the group ${\rm U}(N+L)$. Such…

Neumann series underlie both Krylov methods and algebraic multigrid smoothers. A low-synch modified Gram-Schmidt (MGS)-GMRES algorithm is described that employs a Neumann series to accelerate the projection step. A corollary to the backward…

Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…

We establish rigorous error bounds for prime counting using a truncated Gaussian (TG) kernel in the explicit formula framework. Our main theorem proves that the approximation error remains globally below 1/2 for all sufficiently large…

The Neural Tangent Kernel (NTK) characterizes how a model's state evolves over Gradient Descent. Computing the full NTK matrix is often infeasible, especially for recurrent architectures. Here, we introduce a matrix-free perspective, using…

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…

This paper presents a compression framework for Reservoir Computing that enables systematic design-space exploration of trade-offs among quantization levels, pruning rates, model accuracy, and hardware efficiency. The proposed approach…

To recover a low rank structure from a noisy matrix, truncated singular value decomposition has been extensively used and studied. Recent studies suggested that the signal can be better estimated by shrinking the singular values. We pursue…

Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…

Kernel matrices are crucial in many learning tasks such as support vector machines or kernel ridge regression. The kernel matrix is typically dense and large-scale. Depending on the dimension of the feature space even the computation of all…

We study the statistical distribution of primitive sublattices in the space of lattices $\mathrm{SL}(n,\mathbb Z)\backslash\mathrm{SL}(n,\mathbb R)$. A central difficulty in this area is that the second moment of the counting function for…

Deep learning based methods have dominated super-resolution (SR) field due to their remarkable performance in terms of effectiveness and efficiency. Most of these methods assume that the blur kernel during downsampling is predefined/known…

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…

The rapid and accurate evaluation of convolutions with singular kernels plays crucial roles in a wide range of scientific and engineering applications. Building on the recently introduced Truncated Fourier Filtering method for smooth…

Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…