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The probability Jaccard similarity was recently proposed as a natural generalization of the Jaccard similarity to measure the proximity of sets whose elements are associated with relative frequencies or probabilities. In combination with a…
Embeddings provide compact representations of signals in order to perform efficient inference in a wide variety of tasks. In particular, random projections are common tools to construct Euclidean distance-preserving embeddings, while…
Near-duplicate text alignment is the task of identifying, among the texts in a corpus, all the subsequences (substrings) that are similar to a given query. Traditional approaches rely on seeding-extension-filtering heuristics, which lack…
To get estimators that work within a certain error bound with high probability, a common strategy is to design one that works with constant probability, and then boost the probability using independent repetitions. Important examples of…
We develop a new family of variance reduced stochastic gradient descent methods for minimizing the average of a very large number of smooth functions. Our method --JacSketch-- is motivated by novel developments in randomized numerical…
In their seminal work, Broder \textit{et. al.}~\citep{BroderCFM98} introduces the $\mathrm{minHash}$ algorithm that computes a low-dimensional sketch of high-dimensional binary data that closely approximates pairwise Jaccard similarity.…
High-dimensional sparse data present computational and statistical challenges for supervised learning. We propose compact linear sketches for reducing the dimensionality of the input, followed by a single layer neural network. We show that…
Matrix sketching is a recently developed data compression technique. An input matrix A is efficiently approximated with a smaller matrix B, so that B preserves most of the properties of A up to some guaranteed approximation ratio. In so…
In second-order optimization, a potential bottleneck can be computing the Hessian matrix of the optimized function at every iteration. Randomized sketching has emerged as a powerful technique for constructing estimates of the Hessian which…
This version is ***superseded*** by a full version that can be found at http://www.itu.dk/people/pagh/papers/mining-jour.pdf, which contains stronger theoretical results and fixes a mistake in the reporting of experiments. Abstract:…
Sets have been used for modeling various types of objects (e.g., a document as the set of keywords in it and a customer as the set of the items that she has purchased). Measuring similarity (e.g., Jaccard Index) between sets has been a key…
Consistent sampling is a technique for specifying, in small space, a subset $S$ of a potentially large universe $U$ such that the elements in $S$ satisfy a suitably chosen sampling condition. Given a subset $\mathcal{I}\subseteq U$ it…
This paper presents a new algorithm for calculating hash signatures of sets which can be directly used for Jaccard similarity estimation. The new approach is an improvement over the MinHash algorithm, because it has a better runtime…
Minification is a widely-accepted technique which aims at reducing the size of the code transmitted over the web. We study the problem of minifying Cascading Style Sheets (CSS) --- the de facto language for styling web documents.…
Modern statistical analysis often encounters datasets with large sizes. For these datasets, conventional estimation methods can hardly be used immediately because practitioners often suffer from limited computational resources. In most…
Bipartite networks manifest as a stream of edges that represent transactions, e.g., purchases by retail customers. Many machine learning applications employ neighborhood-based measures to characterize the similarity among the nodes, such as…
We introduce a new sub-linear space sketch---the Weight-Median Sketch---for learning compressed linear classifiers over data streams while supporting the efficient recovery of large-magnitude weights in the model. This enables…
In recent years, network embedding methods have garnered increasing attention because of their effectiveness in various information retrieval tasks. The goal is to learn low-dimensional representations of vertexes in an information network…
In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…
Matrix sketching is a powerful tool for reducing the size of large data matrices. Yet there are fundamental limitations to this size reduction when we want to recover an accurate estimator for a task such as least square regression. We show…