相关论文: Non-Mergeable Sketching for Cardinality Estimation

Randomized sketches of a tensor product of $p$ vectors follow a tradeoff between statistical efficiency and computational acceleration. Commonly used approaches avoid computing the high-dimensional tensor product explicitly, resulting in a…

Given a collection of $m$ sets from a universe $\mathcal{U}$, the Maximum Set Coverage problem consists of finding $k$ sets whose union has largest cardinality. This problem is NP-Hard, but the solution can be approximated by a polynomial…

Hand-drawn sketches are a natural and efficient medium for capturing and conveying ideas. Despite significant advancements in controllable natural image generation, translating freehand sketches into structured, machine-readable diagrams…

We consider sketching algorithms which first quickly compress data by multiplication with a random sketch matrix, and then apply the sketch to quickly solve an optimization problem, e.g., low rank approximation. In the learning-based…

In this work, we present a dimensionality reduction algorithm, aka. sketching, for categorical datasets. Our proposed sketching algorithm Cabin constructs low-dimensional binary sketches from high-dimensional categorical vectors, and our…

We present Sketch 'n Solve, an open-source Python package that implements efficient randomized numerical linear algebra (RandNLA) techniques for solving large-scale least squares problems. While sketch-and-solve algorithms have demonstrated…

In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…

The general applicability and ease of use of the pseudo-marginal Metropolis--Hastings (PMMH) algorithm, and particle Metropolis--Hastings in particular, makes it a popular method for inference on discretely observed Markovian stochastic…

Algorithms in the data stream model use $O(polylog(N))$ space to compute some property of an input of size $N$, and many of these algorithms are implemented and used in practice. However, sketching algorithms in the graph semi-streaming…

Kernel methods are learning algorithms that enjoy solid theoretical foundations while suffering from important computational limitations. Sketching, which consists in looking for solutions among a subspace of reduced dimension, is a well…

We revisit the well-studied problem of approximating a matrix product, $\mathbf{A}^T\mathbf{B}$, based on small space sketches $\mathcal{S}(\mathbf{A})$ and $\mathcal{S}(\mathbf{B})$ of $\mathbf{A} \in \R^{n \times d}$ and $\mathbf{B}\in…

Finding the connected components of a graph is a fundamental problem with uses throughout computer science and engineering. The task of computing connected components becomes more difficult when graphs are very large, or when they are…

We consider hypergraphs on vertices $P\cup R$ where each hyperedge contains exactly one vertex in $P$. Our goal is to select a matching that covers all of $P$, but we allow each selected hyperedge to drop all but an $(1/\alpha)$-fraction of…

We consider sketched approximate matrix multiplication and ridge regression in the novel setting of localized sketching, where at any given point, only part of the data matrix is available. This corresponds to a block diagonal structure on…

This paper considers a new approach to using Markov chain Monte Carlo (MCMC) in contexts where one may adopt multilevel (ML) Monte Carlo. The underlying problem is to approximate expectations w.r.t. an underlying probability measure that is…

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…

A sketch is a probabilistic data structure used to record frequencies of items in a multi-set. Sketches are widely used in various fields, especially those that involve processing and storing data streams. In streaming applications with…

In hypergraphs, an edge that crosses a cut (i.e., a bipartition of nodes) can be split in several ways, depending on how many nodes are placed on each side of the cut. A cardinality-based splitting function assigns a nonnegative cost of…

Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…

This paper considers the problem of cardinality estimation in data stream applications. We present a statistical analysis of probabilistic counting algorithms, focusing on two techniques that use pseudo-random variates to form…