Related papers: Tensor-Based Sketching Method for the Low-Rank App…
In this paper, we show that the bundle method can be applied to solve semidefinite programming problems with a low rank solution without ever constructing a full matrix. To accomplish this, we use recent results from randomly sketching…
We propose a low-rank tensor approach to approximate linear transport and nonlinear Vlasov solutions and their associated flow maps. The approach takes advantage of the fact that the differential operators in the Vlasov equation is tensor…
Deep learning has made profound impacts in the domains of data mining and AI, distinguished by the groundbreaking achievements in numerous real-world applications and the innovative algorithm design philosophy. However, it suffers from the…
We present an efficient low-rank approximation algorithm for non-negative tensors. The algorithm is derived from our two findings: First, we show that rank-1 approximation for tensors can be viewed as a mean-field approximation by treating…
We propose a block coordinate descent type algorithm for estimating the rank of a given tensor. In addition, the algorithm provides the canonical polyadic decomposition of a tensor. In order to estimate the tensor rank we use sparse…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
The low-rank tensor approximation is very promising for the compression of deep neural networks. We propose a new simple and efficient iterative approach, which alternates low-rank factorization with a smart rank selection and fine-tuning.…
We consider the problem of selecting non-zero entries of a matrix $A$ in order to produce a sparse sketch of it, $B$, that minimizes $\|A-B\|_2$. For large $m \times n$ matrices, such that $n \gg m$ (for example, representing $n$…
In the last decade, tensors have shown their potential as valuable tools for various tasks in numerical linear algebra. While most of the research has been focusing on how to compress a given tensor in order to maintain information as well…
While post-training model compression can greatly reduce the inference cost of a deep neural network, uncompressed training still consumes a huge amount of hardware resources, run-time and energy. It is highly desirable to directly train a…
Approximate Nearest Neighbor (ANN) search and Approximate Kernel Density Estimation (A-KDE) are fundamental problems at the core of modern machine learning, with broad applications in data analysis, information systems, and large-scale…
Accounting for the uncertainty in the predictions of modern neural networks is a challenging and important task in many domains. Existing algorithms for uncertainty estimation require modifying the model architecture and training procedure…
Developing high-performance and energy-efficient algorithms for maximum matchings is becoming increasingly important in social network analysis, computational sciences, scheduling, and others. In this work, we propose the first maximum…
A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated…
Recently, low-rank tensor completion has become increasingly attractive in recovering incomplete visual data. Considering a color image or video as a three-dimensional (3D) tensor, existing studies have put forward several definitions of…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…
In this paper, we study the problem of finding a maximum matching in the semi-streaming model when edges arrive in a random order. In the semi-streaming model, an algorithm receives a stream of edges and it is allowed to have a memory of…
In this paper, we propose a novel tensor learning and coding model for third-order data completion. Our model is to learn a data-adaptive dictionary from the given observations, and determine the coding coefficients of third-order tensor…