Related papers: Simpler and Better Cardinality Estimators for Hype…

Cardinality estimation is the task of approximating the number of distinct elements in a large dataset with possibly repeating elements. LogLog and HyperLogLog (c.f. Durand and Flajolet [ESA 2003], Flajolet et al. [Discrete Math Theor.…

This work presents new cardinality estimation methods for data sets recorded by HyperLogLog sketches. A simple derivation of the original estimator was found, that also gives insight how to correct its deficiencies. The result is an…

The information presented in this paper defines LogLog-Beta. LogLog-Beta is a new algorithm for estimating cardinalities based on LogLog counting. The new algorithm uses only one formula and needs no additional bias corrections for the…

Cardinality estimation is perhaps the simplest non-trivial statistical problem that can be solved via sketching. Industrially-deployed sketches like HyperLogLog, MinHash, and PCSA are mergeable, which means that large data sets can be…

This paper presents new methods to estimate the cardinalities of data sets recorded by HyperLogLog sketches. A theoretically motivated extension to the original estimator is presented that eliminates the bias for small and large…

We present HyperLogLogLog, a practical compression of the HyperLogLog sketch that compresses the sketch from $O(m\log\log n)$ bits down to $m \log_2\log_2\log_2 m + O(m+\log\log n)$ bits for estimating the number of distinct elements~$n$…

Cardinality estimation algorithms receive a stream of elements whose order might be arbitrary, with possible repetitions, and return the number of distinct elements. Such algorithms usually seek to minimize the required storage and…

Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…

Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…

In the model of \emph{local computation algorithms} (LCAs), we aim to compute the queried part of the output by examining only a small (sublinear) portion of the input. Many recently developed LCAs on graph problems achieve time and space…

In recent years, \emph{learned cardinality estimation} has emerged as an alternative to traditional query optimization methods: by training machine learning models over observed query performance, learned cardinality estimation techniques…

Semantic segmentation with fine-grained pixel-level accuracy is a fundamental component of a variety of computer vision applications. However, despite the large improvements provided by recent advances in the architectures of convolutional…

Based on some new robust estimators of the covariance matrix, we propose stable versions of Principal Component Analysis (PCA) and we qualify it independently of the dimension of the ambient space. We first provide a robust estimator of the…

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…

Cardinality estimation (CardEst) still remains a challenging problem for DBMS. Recent years have witnessed the success of ML-based cardinality estimators in outperforming traditional methods. However, these solutions suffer from poor…

Graph-based Retrieval Augmented Generation (GraphRAG) extends retrieval-augmented generation to support structured reasoning over complex corpora, but its reliability under resource-constrained, privacy-sensitive deployments remains…

The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

Cardinality estimation algorithms receive a stream of elements, with possible repetitions, and return the number of distinct elements in the stream. Such algorithms seek to minimize the required memory and CPU resource consumption at the…