Related papers: Sparse Partial-Tracing
We study a dynamic version of the implicit trace estimation problem. Given access to an oracle for computing matrix-vector multiplications with a dynamically changing matrix A, our goal is to maintain an accurate approximation to A's trace…
While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…
Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over homogeneous graphs. In heterogeneous graphs such as knowledge graphs, however, sparsification has not been systematically…
Sparse-dense linear algebra is crucial in many domains, but challenging to handle efficiently on CPUs, GPUs, and accelerators alike; multiplications with sparse formats like CSR and CSF require indirect memory lookups. In this work, we…
In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tensor order. We propose an algorithm named Sparse Tensor-train…
We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear…
We present a new algorithm for transposing sparse tensors called Quesadilla. The algorithm converts the sparse tensor data structure to a list of coordinates and sorts it with a fast multi-pass radix algorithm that exploits knowledge of the…
Support estimation (SE) of a sparse signal refers to finding the location indices of the non-zero elements in a sparse representation. Most of the traditional approaches dealing with SE problem are iterative algorithms based on greedy…
Researchers are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix/vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and…
Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the…
We consider the task of approximating a matrix function $f(A)$, where $A$ is a matrix in which only a relatively small number of (not necessarily consecutive) sub- and superdiagonals contain nonzero entries. Approximating $f$ by a…
This paper describes the adaptation of a well-scaling parallel algorithm for computing Morse-Smale segmentations based on path compression to a distributed computational setting. Additionally, we extend the algorithm to efficiently compute…
In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using…
Sparse coding aims to model data vectors as sparse linear combinations of basis elements, but a majority of related studies are restricted to continuous data without spatial or temporal structure. A new model-based sparse coding (MSC)…
Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies.…
Multi-threaded programs are expected to improve responsiveness and conserve resources by dividing an application process into multiple threads for concurrent processing. However, due to scheduling and the interaction of multiple threads,…
We consider the question: what is the abstraction that should be implemented by the computational engine of a machine learning system? Current machine learning systems typically push whole tensors through a series of compute kernels such as…
Recent progress in scaling large models has motivated recommender systems to increase model depth and capacity to better leverage massive behavioral data. However, recommendation inputs are high-dimensional and extremely sparse, and simply…
This chapter focuses on active sensing using sparse arrays. In active sensing applications, such as radar, sonar, wireless communications, and medical ultrasound, a collection of sensors probes the environment by emitting self-generated…
Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…