Related papers: Subspace acceleration for large-scale parameter-de…

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The…

Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular…

With the growing interest and applications in machine learning and data science, finding an efficient method to sparse analysis the high-dimensional data and optimizing a dimension reduction model to extract lower dimensional features has…

Deep learning models incorporating linear SSMs have gained attention for capturing long-range dependencies in sequential data. However, their large parameter sizes pose challenges for deployment on resource-constrained devices. In this…

We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…

In this paper, we propose a subspace method based on neural networks for eigenvalue problems with high accuracy and low cost. We first construct a neural network-based orthogonal basis by some deep learning method and dimensionality…

A two dimensional eigenvalue problem (2DEVP) of a Hermitian matrix pair $(A, C)$ is introduced in this paper. The 2DEVP can be viewed as a linear algebraic formulation of the well-known eigenvalue optimization problem of the parameter…

One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…

In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…

Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…

Built upon the decision tree (DT) classification and regression idea, the subspace learning machine (SLM) has been recently proposed to offer higher performance in general classification and regression tasks. Its performance improvement is…

Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…

Approximate Bayesian Computation (ABC) methods have become essential tools for performing inference when likelihood functions are intractable or computationally prohibitive. However, their scalability remains a major challenge in…

We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the…

Dimension reduction provides a useful tool for analyzing high dimensional data. The recently developed \textit{Envelope} method is a parsimonious version of the classical multivariate regression model through identifying a minimal reducing…

Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of…

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…

The Adaptive Metropolis (AM) algorithm is based on the symmetric random-walk Metropolis algorithm. The proposal distribution has the following time-dependent covariance matrix at step $n+1$ \[ S_n = Cov(X_1,...,X_n) + \epsilon I, \] that…

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively.…

Sequential robot manipulation tasks require finding collision-free trajectories that satisfy geometric constraints across multiple object interactions in potentially high-dimensional configuration spaces. Solving these problems in real-time…