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

We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…

We present function preserving projections (FPP), a scalable linear projection technique for discovering interpretable relationships in high-dimensional data. Conventional dimension reduction methods aim to maximally preserve the global…

Given a dataset of points in a metric space and an integer $k$, a diversity maximization problem requires determining a subset of $k$ points maximizing some diversity objective measure, e.g., the minimum or the average distance between two…

Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…

The Count-Min sketch is an important and well-studied data summarization method. It allows one to estimate the count of any item in a stream using a small, fixed size data sketch. However, the accuracy of the sketch depends on…

Given a persistence diagram with $n$ points, we give an algorithm that produces a sequence of $n$ persistence diagrams converging in bottleneck distance to the input diagram, the $i$th of which has $i$ distinct (weighted) points and is a…

Fixpoints are ubiquitous in computer science and when dealing with quantitative semantics and verification one often considers least fixpoints of (higher-dimensional) functions over the non-negative reals. We show how to approximate the…

The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…

We pursue a study of the Generalized Demand Matching problem, a common generalization of the $b$-Matching and Knapsack problems. Here, we are given a graph with vertex capacities, edge profits, and asymmetric demands on the edges. The goal…

In rapid and massive data streams, it is often not possible to estimate the frequency of items with complete accuracy. To perform the operation in a reasonable amount of space and with sufficiently low latency, approximated methods are…

Given a labeled graph, the frequent-subgraph mining (FSM) problem asks to find all the $k$-vertex subgraphs that appear with frequency greater than a given threshold. FSM has numerous applications ranging from biology to network science, as…

We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…

The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithmsfor approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a…

Tensor network contraction is a fundamental mathematical operation that generalizes the dot product and matrix multiplication. It finds applications in numerous domains, such as database systems, graph theory, machine learning, probability…

An $\varepsilon$-approximate quantile sketch over a stream of $n$ inputs approximates the rank of any query point $q$ - that is, the number of input points less than $q$ - up to an additive error of $\varepsilon n$, generally with some…

Constrained least squares problems arise in many applications. Their memory and computation costs are expensive in practice involving high-dimensional input data. We employ the so-called "sketching" strategy to project the least squares…

Categorical attributes are those that can take a discrete set of values, e.g., colours. This work is about compressing vectors over categorical attributes to low-dimension discrete vectors. The current hash-based methods compressing vectors…

This paper develops the sketching (i.e., randomized dimension reduction) theory for real algebraic varieties and images of polynomial maps, including, e.g., the set of low rank tensors and tensor networks. Through the lens of norming sets,…

This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…

Sketching and stochastic gradient methods are arguably the most common techniques to derive efficient large scale learning algorithms. In this paper, we investigate their application in the context of nonparametric statistical learning.…