Related papers: Fast Regression with an $\ell_\infty$ Guarantee
Recent advancement of the WWW, IOT, social network, e-commerce, etc. have generated a large volume of data. These datasets are mostly represented by high dimensional and sparse datasets. Many fundamental subroutines of common data analytic…
Many data sources can be interpreted as time-series, and a key problem is to identify which pairs out of a large collection of signals are highly correlated. We expect that there will be few, large, interesting correlations, while most…
Matrices have become essential data representations for many large-scale problems in data analytics, and hence matrix sketching is a critical task. Although much research has focused on improving the error/size tradeoff under various…
Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…
Researchers may perform regressions using a sketch of data of size $m$ instead of the full sample of size $n$ for a variety of reasons. This paper considers the case when the regression errors do not have constant variance and…
Elastic-Sketch is a hash-based data structure for counting item's appearances in a data stream, and it has been empirically shown to achieve a better memory-accuracy trade-off compared to classical methods. This algorithm combines a heavy…
We present new adaptive sampling rules for the sketch-and-project method for solving linear systems. To deduce our new sampling rules, we first show how the progress of one step of the sketch-and-project method depends directly on a…
Large-sample data became prevalent as data acquisition became cheaper and easier. While a large sample size has theoretical advantages for many statistical methods, it presents computational challenges. Sketching, or compression, is a…
We introduce a new sub-linear space sketch---the Weight-Median Sketch---for learning compressed linear classifiers over data streams while supporting the efficient recovery of large-magnitude weights in the model. This enables…
The aim of this paper is two-fold: firstly, to present subspace embedding properties for $s$-hashing sketching matrices, with $s\geq 1$, that are optimal in the projection dimension $m$ of the sketch, namely, $m=\mathcal{O}(d)$, where $d$…
Randomized subspace embedding methods have had a great impact on the solution of a linear least squares (LS) problem by reducing its row dimension, leading to a randomized or sketched LS (sLS) problem, and use the solution of the sLS…
Many popular first-order optimization methods (e.g., Momentum, AdaGrad, Adam) accelerate the convergence rate of deep learning models. However, these algorithms require auxiliary parameters, which cost additional memory proportional to the…
We introduce a new approach for applying sampling-based sketches to two and three mode tensors. We illustrate our technique to construct sketches for the classical problems of $\ell_0$ sampling and producing $\ell_1$ embeddings. In both…
Graph Neural Networks learn on graph-structured data by iteratively aggregating local neighborhood information. While this local message passing paradigm imparts a powerful inductive bias and exploits graph sparsity, it also yields three…
The Neural Tangent Kernel (NTK) characterizes the behavior of infinitely-wide neural networks trained under least squares loss by gradient descent. Recent works also report that NTK regression can outperform finitely-wide neural networks…
Subgraph counting is a fundamental primitive in graph processing, with applications in social network analysis (e.g., estimating the clustering coefficient of a graph), database processing and other areas. The space complexity of subgraph…
Motivated by the randomized sketch to solve a variety of problems in scientific computation, we improve both the maximal weighted residual Kaczmarz method and the randomized block average Kaczmarz method using two new randomized sketch…
The randomized coordinate descent (RCD) method is a classical algorithm with simple, lightweight iterations that is widely used for various optimization problems, including the solution of positive semidefinite linear systems. As a linear…
We consider online statistical inference of constrained stochastic nonlinear optimization problems. We apply the Stochastic Sequential Quadratic Programming (StoSQP) method to solve these problems, which can be regarded as applying…
Stream monitoring is fundamental in many data stream applications, such as financial data trackers, security, anomaly detection, and load balancing. In that respect, quantiles are of particular interest, as they often capture the user's…