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 problem of inner product estimation. We further develop this finding by introducing and analyzing two alternative sampling-based methods. In contrast to the computationally expensive algorithm in Bessa et al., our methods run in linear time (to compute the sketch) and perform better in practice, significantly beating linear sketching on a variety of tasks. For example, they provide state-of-the-art results for estimating the correlation between columns in unjoined tables, a problem that we show how to reduce to inner product estimation in a black-box way. While based on known sampling techniques (threshold and priority sampling) we introduce significant new theoretical analysis to prove approximation guarantees for our methods.

We present a new approach for independently computing compact sketches that can be used to approximate the inner product between pairs of high-dimensional vectors. Based on the Weighted MinHash algorithm, our approach admits strong accuracy guarantees that improve on the guarantees of popular linear sketching approaches for inner product estimation, such as CountSketch and Johnson-Lindenstrauss projection. Specifically, while our method exactly matches linear sketching for dense vectors, it yields significantly lower error for sparse vectors with limited overlap between non-zero entries. Such vectors arise in many applications involving sparse data, as well as in increasingly popular dataset search applications, where inner products are used to estimate data covariance, conditional means, and other quantities involving columns in unjoined tables. We complement our theoretical results by showing that our approach empirically outperforms existing linear sketches and unweighted hashing-based sketches for sparse vectors.

Dataset search is emerging as a critical capability in both research and industry: it has spurred many novel applications, ranging from the enrichment of analyses of real-world phenomena to the improvement of machine learning models. Recent research in this field has explored a new class of data-driven queries: queries consist of datasets and retrieve, from a large collection, related datasets. In this paper, we study a specific type of data-driven query that supports relational data augmentation through numerical data relationships: given an input query table, find the top-k tables that are both joinable with it and contain columns that are correlated with a column in the query. We propose a novel hashing scheme that allows the construction of a sketch-based index to support efficient correlated table search. We show that our proposed approach is effective and efficient, and achieves better trade-offs that significantly improve both the ranking accuracy and recall compared to the state-of-the-art solutions.

The increasing availability of structured datasets, from Web tables and open-data portals to enterprise data, opens up opportunities to enrich analytics and improve machine learning models through relational data augmentation. In this paper, we introduce a new class of data augmentation queries: join-correlation queries. Given a column Q and a join column KQ from a query table TQ, retrieve tables TX in a dataset collection such that TX is joinable with TQ on KQ and there is a column C ∈ TX such that Q is correlated with C. A naïve approach to evaluate these queries, which first finds joinable tables and then explicitly joins and computes correlations between Q and all columns of the discovered tables, is prohibitively expensive. To efficiently support correlated column discovery, we 1) propose a sketching method that enables the construction of an index for a large number of tables and that provides accurate estimates for join-correlation queries, and 2) explore different scoring strategies that effectively rank the query results based on how well the columns are correlated with the query. We carry out a detailed experimental evaluation, using both synthetic and real data, which shows that our sketches attain high accuracy and the scoring strategies lead to high-quality rankings.

In this paper, we make a first attempt to incorporate both commuting demand and transit network connectivity in bus route planning (CT-Bus), and formulate it as a constrained optimization problem: planning a new bus route with k edges over an existing transit network without building new bus stops to maximize a linear aggregation of commuting demand and connectivity of the transit network. We prove the NP-hardness of CT-Bus and propose an expansion-based greedy algorithm that iteratively scans potential candidate paths in the network. To boost the efficiency of computing the connectivity of new networks with candidate paths, we convert it to a matrix trace estimation problem and employ a Lanczos method to estimate the natural connectivity of the transit network with a guaranteed error bound. Furthermore, we derive upper bounds on the objective values and use them to greedily select candidates for expansion. Our experiments conducted on real-world transit networks in New York City and Chicago verify the efficiency, effectiveness, and scalability of our algorithms.

While social networks have increased the diversity of ideas and information available to users, they are also blamed for increasing the polarization of user opinions. Eli Pariser's "filter bubble" hypothesis [55] explains this counterintuitive phenomenon by linking user polarization to algorithmic filtering: to increase user engagement, social media companies connect users with ideas they are already likely to agree with, thus creating echo chambers of users with very similar beliefs.

The rise of social media and online social networks has been a disruptive force in society. Opinions are increasingly shaped by interactions on online social media, and social phenomena including disagreement and polarization are now tightly woven into everyday life. In this work we initiate the study of the following question: \beginquotation \noindent Given n agents, each with its own initial opinion that reflects its core value on a topic, and an opinion dynamics model, what is the structure of a social network that minimizes \em disagreementand \em controversy simultaneously? \endquotation \noindent This question is central to recommender systems: should a recommender system prefer a link suggestion between two online users with similar mindsets in order to keep disagreement low, or between two users with different opinions in order to expose each to the others viewpoint of the world, and decrease overall levels of polarization and controversy? Such decisions have an important global effect on society \citewilliams2007social. Our contributions include a mathematical formalization of this question as an optimization problem and an exact, time-efficient algorithm. We also prove that there always exists a graph with $O(n/ε^2)$ edges that is a $(1+ε)$ approximation to the optimum. Our formulation is an instance of optimization over \em graph topologies, see also \citeboyd2004fastest,daitch2009fitting,sun2006fastest. Furthermore, for a given graph, we show how to optimize the same objective over the agents» innate opinions in polynomial time. Finally, we perform an empirical study of our proposed methods on synthetic and real-world data that verify their value as mining tools to better understand the trade-off between of disagreement and polarization. We find that there is a lot of space to reduce both controversy and disagreement in real-world networks; for instance, on a Reddit network where users exchange comments on politics, our methods achieve a reduction in controversy and disagreement of the order $6.2 \times 10^4$.