相关论文: Weighted Inner Products for GMRES and GMRES-DR

The incorporation of generative models as regularisers within variational formulations for inverse problems has proven effective across numerous image reconstruction tasks. However, the resulting optimisation problem is often non-convex and…

Recommender Systems (RS), as an efficient tool to discover users' interested items from a very large corpus, has attracted more and more attention from academia and industry. As the initial stage of RS, large-scale matching is fundamental…

This paper develops a large-scale inference approach for the regularization of stock return covariance matrices. The framework allows for the presence of heavy tails and multivariate GARCH-type effects of unknown form among the stock…

Quantization of neural networks has become common practice, driven by the need for efficient implementations of deep neural networks on embedded devices. In this paper, we exploit an oft-overlooked degree of freedom in most networks - for a…

Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…

In this work, we revisit nonlinear generalized minimal residual method (NGMRES) applied to nonlinear problems. NGMRES is used to accelerate the convergence of fixed-point iterations, which can substantially improve the performance of the…

The minibatch stochastic gradient descent method (SGD) is widely applied in deep learning due to its efficiency and scalability that enable training deep networks with a large volume of data. Particularly in the distributed setting, SGD is…

This paper explores the problem of generalized phase retrieval, which involves reconstructing a length-$n$ signal $\bm{x}$ from its $m$ phaseless samples $y_k = \left|\langle \bm{a}_k,\bm{x}\rangle\right|^2$, where $k = 1,2,...,m$, and…

Gradient descent dynamics on the deep matrix factorization problem is extensively studied as a simplified theoretical model for deep neural networks. Although the convergence theory for two-layer matrix factorization is well-established, no…

We provide the first global model recovery results for the IRLS (iteratively reweighted least squares) heuristic for robust regression problems. IRLS is known to offer excellent performance, despite bad initializations and data corruption,…

In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…

In many learning problems, the training and testing data follow different distributions and a particularly common situation is the \textit{covariate shift}. To correct for sampling biases, most approaches, including the popular kernel mean…

In this article we show how power transformations can be used as a common framework for the derivation of local term weights. We found that under some parametric conditions, BM25 and inverse regression produce equivalent results. As a…

A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $\varphi$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with…

The discretization of convection-diffusion equations by implicit or semi-implicit methods leads to a sequence of linear systems usually solved by iterative linear solvers such as GMRES. Many techniques bearing the name of \emph{recycling…

The modified Gram-Schmidt (MGS) orthogonalization is one of the most well-used algorithms for computing the thin QR factorization. MGS can be straightforwardly extended to a non-standard inner product with respect to a symmetric positive…

In this paper, we consider an approximation method, and a novel general analysis, for second-order elliptic differential equations with heterogeneous multiscale coefficients. We obtain convergence of the Generalized Multi-scale Finite…

The inputs and/or outputs of some neural nets are weight matrices of other neural nets. Indirect encodings or end-to-end compression of weight matrices could help to scale such approaches. Our goal is to open a discussion on this topic,…

Recovering unbiased kinetic and thermodynamic observables from the enhanced sampling simulations is a central challenge in rare-event sampling. Classical Girsanov Reweighting (GR) offers a principled solution by yielding exact pathwise…

Learning individualized treatment rules (ITRs) is an important topic in precision medicine. Current literature mainly focuses on deriving ITRs from a single source population. We consider the observational data setting when the source…