相关论文: Efficient Data-Driven Leverage Score Sampling Algo…
We study the problem of finding the Lowner-John ellipsoid, i.e., an ellipsoid with minimum volume that contains a given convex set. We reformulate the problem as a generalized copositive program, and use that reformulation to derive…
We revisit the problem of sketching using approximate leverage scores for matrix least squares problems of the form $\| AX - B \|_F^2$ where the design matrix $A \in \mathbb{R}^{N \times r}$ is tall and skinny with $N \gg r$. We derive the…
Recent multi-view subspace clustering achieves impressive results utilizing deep networks, where the self-expressive correlation is typically modeled by a fully connected (FC) layer. However, they still suffer from two limitations. i) The…
The article considers minimization of the expectation of convex function. Problems of this type often arise in machine learning and a number of other applications. In practice, stochastic gradient descent (SGD) and similar procedures are…
We apply methods from randomized numerical linear algebra (RandNLA) to develop improved algorithms for the analysis of large-scale time series data. We first develop a new fast algorithm to estimate the leverage scores of an autoregressive…
Leverage score is a fundamental problem in machine learning and theoretical computer science. It has extensive applications in regression analysis, randomized algorithms, and neural network inversion. Despite leverage scores are widely used…
In this paper, we develop the notion of evidence lower bound difference (ELBD), based on which an efficient score algorithm is presented to implement feature selection on latent variables of VAE and its variants. Further, we propose weak…
Random features provide a practical framework for large-scale kernel approximation and supervised learning. It has been shown that data-dependent sampling of random features using leverage scores can significantly reduce the number of…
This paper explores an energy-modified leverage sampling strategy for matrix completion in radio map construction. The main goal is to address potential identifiability issues in matrix completion with sparse observations by using a…
Suppose a matrix $A \in \mathbb{R}^{m \times n}$ of rank $r$ with singular value decomposition $A = U_{A}\Sigma_{A} V_{A}^{T}$, where $U_{A} \in \mathbb{R}^{m \times r}$, $V_{A} \in \mathbb{R}^{n \times r}$ are orthonormal and $\Sigma_{A}…
A major hurdle in machine learning is scalability to massive datasets. Approaches to overcome this hurdle include compression of the data matrix and distributing the computations. \textit{Leverage score sampling} provides a compressed…
Ridge leverage scores provide a balance between low-rank approximation and regularization, and are ubiquitous in randomized linear algebra and machine learning. Deterministic algorithms are also of interest in the moderately big data…
LP-type problems such as the Minimum Enclosing Ball (MEB), Linear Support Vector Machine (SVM), Linear Programming (LP), and Semidefinite Programming (SDP) are fundamental combinatorial optimization problems, with many important…
Tensor Train~(TT) decomposition is widely used in the machine learning and quantum physics communities as a popular tool to efficiently compress high-dimensional tensor data. In this paper, we propose an efficient algorithm to accelerate…
For optimization on large-scale data, exactly calculating its solution may be computationally difficulty because of the large size of the data. In this paper we consider subsampled optimization for fast approximating the exact solution. In…
We give a faster algorithm for computing an approximate John ellipsoid around $n$ points in $d$ dimensions. The best known prior algorithms are based on repeatedly computing the leverage scores of the points and reweighting them by these…
We propose a sampling-based method for computing the tensor ring (TR) decomposition of a data tensor. The method uses leverage score sampled alternating least squares to fit the TR cores in an iterative fashion. By taking advantage of the…
The demand of computational resources for the modeling process increases as the scale of the datasets does, since traditional approaches for regression involve inverting huge data matrices. The main problem relies on the large data size,…
The low-rank canonical polyadic tensor decomposition is useful in data analysis and can be computed by solving a sequence of overdetermined least squares subproblems. Motivated by consideration of sparse tensors, we propose sketching each…
We present a machine learning approach to the solution of chance constrained optimizations in the context of voltage regulation problems in power system operation. The novelty of our approach resides in approximating the feasible region of…