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A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \in \mathbb{R}^{N\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two…
In prior work, Gupta et al. (SPAA 2022) presented a distributed algorithm for multiplying sparse $n \times n$ matrices, using $n$ computers. They assumed that the input matrices are uniformly sparse--there are at most $d$ non-zeros in each…
Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the…
Biclustering is an unsupervised machine-learning approach aiming to cluster rows and columns simultaneously in a data matrix. Several biclustering algorithms have been proposed for handling numeric datasets. However, real-world data mining…
CUR matrix decomposition is a randomized algorithm that can efficiently compute the low rank approximation for a given rectangle matrix. One limitation with the existing CUR algorithms is that they require an access to the full matrix A for…
We consider a variant of regression problem, where the correspondence between input and output data is not available. Such shuffled data is commonly observed in many real world problems. Taking flow cytometry as an example, the measuring…
The central aim in this paper is to address variable selection questions in nonlinear and nonparametric regression. Motivated by statistical genetics, where nonlinear interactions are of particular interest, we introduce a novel and…
The aim of this research is twofold: Firstly, to model and solve a complex nurse scheduling problem with an integer programming formulation and evolutionary algorithms. Secondly, to detail a novel statistical method of comparing and hence…
The presence of missing entries in data often creates challenges for pattern recognition algorithms. Traditional algorithms for clustering data assume that all the feature values are known for every data point. We propose a method to…
The series-parallel (active) redundancy allocation problem with mixed components (RAP) involves setting reliable objectives for components or subsystems to meet the resource consumption constraint, e.g., the total cost. RAP has been an…
Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…
In this paper, we derive new computational techniques for residue number systems (RNS) based Barrett algorithm (BA). The focus of the work is an algorithm that carries out the entire computation using only modular arithmetic without…
Amidst rising appreciation for privacy and data usage rights, researchers have increasingly acknowledged the principle of data minimization, which holds that the accessibility, collection, and retention of subjects' data should be kept to…
Multiplying matrices is among the most fundamental and compute-intensive operations in machine learning. Consequently, there has been significant work on efficiently approximating matrix multiplies. We introduce a learning-based algorithm…
An important problem in training deep networks with high capacity is to ensure that the trained network works well when presented with new inputs outside the training dataset. Dropout is an effective regularization technique to boost the…
We consider the problem of computing the rank of an m x n matrix A over a field. We present a randomized algorithm to find a set of r = rank(A) linearly independent columns in \~O(|A| + r^\omega) field operations, where |A| denotes the…
The Random Batch Method (RBM) is an effective technique to reduce the computational complexity when solving certain stochastic differential problems (SDEs) involving interacting particles. It can transform the computational complexity from…
Matrix completion is often applied to data with entries missing not at random (MNAR). For example, consider a recommendation system where users tend to only reveal ratings for items they like. In this case, a matrix completion method that…
Standard machine learning models optimized for average performance often fail on minority subgroups and lack robustness to distribution shifts. This challenge worsens when subgroups are latent and affected by complex interactions among…