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Dynamic graph clustering aims to detect and track time-varying clusters in dynamic graphs, revealing the evolutionary mechanisms of complex real-world dynamic systems. Matrix factorization-based methods are promising approaches for this…
This paper introduces a Factor Augmented Sparse Throughput (FAST) model that utilizes both latent factors and sparse idiosyncratic components for nonparametric regression. The FAST model bridges factor models on one end and sparse…
The Variable Block Row (VBR) format is an influential blocked sparse matrix format designed for matrices with shared sparsity structure between adjacent rows and columns. VBR groups adjacent rows and columns, storing the resulting blocks…
Hypergraph partitioning is a recurring NP-hard problem in engineering; its efficient solution at scale hinges on parallelism. This work proposes a GPU-centric algorithm for multi-level hypergraph partitioning aimed at a specific set of…
We study exact sparse linear regression with an $\ell_0-\ell_2$ penalty and develop a branch-and-bound (BnB) algorithm explicitly designed for GPU execution. Starting from a perspective reformulation, we derive an interval relaxation that…
A new hybrid algorithm for LDU-factorization for large sparse matrix combining iterative solver, which can keep the same accuracy as the classical factorization, is proposed. The last Schur complement will be generated by iterative solver…
Incomplete LU factorizations of sparse matrices are widely used as preconditioners in Krylov subspace methods to speed up solving linear systems. Unfortunately, computing the preconditioner itself can be time-consuming and sensitive to…
We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…
We describe a second-order accurate approach to sparsifying the off-diagonal blocks in the hierarchical approximate factorizations of sparse symmetric positive definite matrices. The norm of the error made by the new approach depends…
Given matrices $X,Y \in R^{n \times K}$ and $S \in R^{K \times K}$ with positive elements, this paper proposes an algorithm fastRG to sample a sparse matrix $A$ with low rank expectation $E(A) = XSY^T$ and independent Poisson elements. This…
The Fast Approximate BLock-Encoding algorithm (FABLE) is a technique to block-encode arbitrary $N\times N$ dense matrices into quantum circuits using at most $O(N^2)$ one and two-qubit gates and $\mathcal{O}(N^2\log{N})$ classical…
Large language models (LLMs) have demonstrated remarkable performance across a wide range of language processing tasks. However, this success comes at the cost of substantial computation and memory requirements, which significantly impedes…
Scalable sparse LU factorization is critical for efficient numerical simulation of circuits and electrical power grids. In this work, we present a new scalable sparse direct solver called Basker. Basker introduces a new algorithm to…
Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…
This paper proposes a new distributed algorithm for solving linear systems associated with a sparse graph under a generalised diagonal dominance assumption. The algorithm runs iteratively on each node of the graph, with low complexities on…
Nowadays, increasingly larger Deep Neural Networks (DNNs) are being developed, trained, and utilized. These networks require significant computational resources, putting a strain on both advanced and limited devices. Our solution is to…
The rapidly growing parameter volume of deep neural networks (DNNs) hinders the artificial intelligence applications on resource constrained devices, such as mobile and wearable devices. Neural network pruning, as one of the mainstream…
The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…
Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…
Many machine learning models, including those with non-smooth regularizers, can be formulated as consensus optimization problems, which can be solved by the alternating direction method of multipliers (ADMM). Many recent efforts have been…