Related papers: Unifying Matrix Data Structures: Simplifying and S…
The dynamic matrix inverse problem is to maintain the inverse of a matrix undergoing element and column updates. It is the main subroutine behind the best algorithms for many dynamic problems whose complexity is not yet well-understood,…
We present a general framework that utilizes different efficient data structures to improve various sparsification problems involving an iterative process. We also provide insights and characterization for different iterative process, and…
We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…
Over the past two decades, topological data analysis has emerged as a field of applied mathematics with new applications and algorithmic developments appearing rapidly. Two fundamental computations in this field are persistent homology and…
Graph pattern matching algorithms to handle million-scale dynamic graphs are widely used in many applications such as social network analytics and suspicious transaction detections from financial networks. On the other hand, the computation…
Matrix reduction is the standard procedure for computing the persistent homology of a filtered simplicial complex with $m$ simplices. Its output is a particular decomposition of the total boundary matrix, from which the persistence diagrams…
Parallel dataflow systems are a central part of most analytic pipelines for big data. The iterative nature of many analysis and machine learning algorithms, however, is still a challenge for current systems. While certain types of bulk…
In today's data driven world, storing, processing, and gleaning insights from large-scale data are major challenges. Data compression is often required in order to store large amounts of high-dimensional data, and thus, efficient inference…
Several recently devised machine learning (ML) algorithms have shown improved accuracy for various predictive problems. Model searches, which explore to find an optimal ML algorithm and hyperparameter values for the target problem, play a…
Nonnegative matrix factorization (NMF) is a powerful tool in data exploratory analysis by discovering the hidden features and part-based patterns from high-dimensional data. NMF and its variants have been successfully applied into diverse…
Motivated by recent Linear Programming solvers, we design dynamic data structures for maintaining the inverse of an $n\times n$ real matrix under $\textit{low-rank}$ updates, with polynomially faster amortized running time. Our data…
As an important problem in modern data analytics, classification has witnessed varieties of applications from different domains. Different from conventional classification approaches, fair classification concerns the issues of unintentional…
In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…
Deep neural networks employ specialized architectures for vision, sequential and language tasks, yet this proliferation obscures their underlying commonalities. We introduce a unified matrix-order framework that casts convolutional,…
Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
Many iterative algorithms in optimization, computational geometry, computer algebra, and other areas of computer science require repeated computation of some algebraic expression whose input changes slightly from one iteration to the next.…
Transformers have demonstrated effectiveness in in-context solving data-fitting problems from various (latent) models, as reported by Garg et al. However, the absence of an inherent iterative structure in the transformer architecture…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
Persistent homology is a topological feature used in a variety of applications such as generating features for data analysis and penalizing optimization problems. We develop an approach to accelerate persistent homology computations…