相关论文: Non-Mergeable Sketching for Cardinality Estimation

With the rapid progress of Multimodal LLMs, evaluating their mathematical reasoning capabilities has become an increasingly important research direction. In particular, visual-textual mathematical reasoning serves as a key indicator of an…

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…

Benchmark data sets are a cornerstone of machine learning development and applications, ensuring new methods are robust, reliable and competitive. The relative rarity of benchmark sets in computational science, due to the uniqueness of the…

Recently, Bessa et al. (PODS 2023) showed that sketches based on coordinated weighted sampling theoretically and empirically outperform popular linear sketching methods like Johnson-Lindentrauss projection and CountSketch for the ubiquitous…

The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one…

We introduce a technique for estimating a structured covariance matrix from observations of a random vector which have been sketched. Each observed random vector $\boldsymbol{x}_t$ is reduced to a single number by taking its inner product…

Recent developments in parallel Markov chain Monte Carlo (MCMC) algorithms allow us to run thousands of chains almost as quickly as a single chain, using hardware accelerators such as GPUs. While each chain still needs to forget its initial…

In this paper, we revisit the classic CountSketch method, which is a sparse, random projection that transforms a (high-dimensional) Euclidean vector $v$ to a vector of dimension $(2t-1) s$, where $t, s > 0$ are integer parameters. It is…

Learning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. We propose a "compressive learning" framework where we estimate model parameters from a sketch of the training data. This sketch…

General SVG modeling remains challenging due to fragmented datasets, limited transferability of methods across tasks, and the difficulty of handling structural complexity. In response, we leverage the strong transfer and generalization…

Cardinality estimation - calculating the number of distinct elements in a stream - is a longstanding problem with applications from networking to bioinformatics. HyperLogLog (HLL), the prevailing standard, has a well-known error spike in…

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…

Randomized subspace approximation with "matrix sketching" is an effective approach for constructing approximate partial singular value decompositions (SVDs) of large matrices. The performance of such techniques has been extensively…

In collaborative software development, program merging is the mechanism to integrate changes from multiple programmers. Merge algorithms in modern version control systems report a conflict when changes interfere textually. Merge conflicts…

GraphSPME is an open source Python, R and C++ header-only package implement-ing non-parametric sparse precision matrix estimation along with asymptotic Stein-type shrinkage estimation of the covariance matrix. The user defines a potential…

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…

In all state-of-the-art sketching and coreset techniques for clustering, as well as in the best known fixed-parameter tractable approximation algorithms, randomness plays a key role. For the classic $k$-median and $k$-means problems, there…

We introduce Deep Sketches, which are compact models of databases that allow us to estimate the result sizes of SQL queries. Deep Sketches are powered by a new deep learning approach to cardinality estimation that can capture correlations…

We study the classic Max-Cut problem under multiple cardinality constraints, which we refer to as the Constrained Max-Cut problem. Given a graph $G=(V, E)$, a partition of the vertices into $c$ disjoint parts $V_1, \ldots, V_c$, and…

We describe a new cardinality estimation algorithm that is extremely space-efficient. It applies one of three novel estimators to the compressed state of the Flajolet-Martin-85 coupon collection process. In an apples-to-apples empirical…