相关论文: Approximate $\mathbb{F}_2$-Sketching of Valuation …

In the turnstile streaming model, a dynamic vector $\mathbf{x}=(\mathbf{x}_1,\ldots,\mathbf{x}_n)\in \mathbb{Z}^n$ is updated by a stream of entry-wise increments/decrements. Let $f\colon\mathbb{Z}\to \mathbb{R}_+$ be a symmetric function…

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…

In this paper, we show that if the optimization function is restricted-strongly-convex (RSC) and restricted-smooth (RSM) -- a rich subclass of weakly submodular functions -- then a streaming algorithm with constant factor approximation…

Indexing of static and dynamic sets is fundamental to a large set of applications such as information retrieval and caching. Denoting the characteristic vector of the set by B, we consider the problem of encoding sets and multisets to…

Histograms, i.e., piece-wise constant approximations, are a popular tool used to represent data distributions. Traditionally, the difference between the histogram and the underlying distribution (i.e., the approximation error) is measured…

In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within…

Many dynamic applications are built upon large network infrastructures, such as social networks, communication networks, biological networks and the Web. Such applications create data that can be naturally modeled as graph streams, in which…

\begin{abstract} The frequencies of the elements in a data stream are an important statistical measure and the task of estimating them arises in many applications within data analysis and machine learning. Two of the most popular algorithms…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

We consider massive distributed datasets that consist of elements modeled as key-value pairs and the task of computing statistics or aggregates where the contribution of each key is weighted by a function of its frequency (sum of values of…

Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…

Tracking and approximating data matrices in streaming fashion is a fundamental challenge. The problem requires more care and attention when data comes from multiple distributed sites, each receiving a stream of data. This paper considers…

Many relevant machine learning and scientific computing tasks involve high-dimensional linear operators accessible only via costly matrix-vector products. In this context, recent advances in sketched methods have enabled the construction of…

Graph Neural Networks (GNNs) are widely applied to graph learning problems such as node classification. When scaling up the underlying graphs of GNNs to a larger size, we are forced to either train on the complete graph and keep the full…

A technique introduced by Indyk and Woodruff [STOC 2005] has inspired several recent advances in data-stream algorithms. We show that a number of these results follow easily from the application of a single probabilistic method called…

We consider approximation of functions of $s$ variables, where $s$ is very large or infinite, that belong to weighted anchored spaces. We study when such functions can be approximated by algorithms designed for functions with only very…

We present space-efficient linear sketches for estimating trimmed statistics of an $n$-dimensional frequency vector $x$, e.g., the sum of $p$-th powers of the largest $k$ frequencies (i.e., entries) in absolute value, or the $k$-trimmed…

Consider an $s$-dimensional function being evaluated at $n$ points of a low discrepancy sequence (LDS), where the objective is to approximate the one-dimensional functions that result from integrating out $(s-1)$ variables. Here, the…

As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…

We give a sketching-based iterative algorithm that computes a $1+\varepsilon$ approximate solution for the ridge regression problem $\min_x \|Ax-b\|_2^2 +\lambda\|x\|_2^2$ where $A \in R^{n \times d}$ with $d \ge n$. Our algorithm, for a…