RRR: Rank-Regret Representative

Selecting the best items in a dataset is a common task in data exploration. However, the concept of "best" lies in the eyes of the beholder: different users may consider different attributes more important, and hence arrive at different rankings. Nevertheless, one can remove "dominated" items and create a "representative" subset of the data set, comprising the "best items" in it. A Pareto-optimal representative is guaranteed to contain the best item of each possible ranking, but it can be almost as big as the full data. Representative can be found if we relax the requirement to include the best item for every possible user, and instead just limit the users' "regret". Existing work defines regret as the loss in score by limiting consideration to the representative instead of the full data set, for any chosen ranking function. However, the score is often not a meaningful number and users may not understand its absolute value. Sometimes small ranges in score can include large fractions of the data set. In contrast, users do understand the notion of rank ordering. Therefore, alternatively, we consider the position of the items in the ranked list for defining the regret and propose the {\em rank-regret representative} as the minimal subset of the data containing at least one of the top-$k$ of any possible ranking function. This problem is NP-complete. We use the geometric interpretation of items to bound their ranks on ranges of functions and to utilize combinatorial geometry notions for developing effective and efficient approximation algorithms for the problem. Experiments on real datasets demonstrate that we can efficiently find small subsets with small rank-regrets

Using Set Covering to Generate Databases for Holistic Steganalysis

Within an operational framework, covers used by a steganographer are likely to come from different sensors and different processing pipelines than the ones used by researchers for training their steganalysis models. Thus, a performance gap is unavoidable when it comes to out-of-distributions covers, an extremely frequent scenario called Cover Source Mismatch (CSM). Here, we explore a grid of processing pipelines to study the origins of CSM, to better understand it, and to better tackle it. A set-covering greedy algorithm is used to select representative pipelines minimizing the maximum regret between the representative and the pipelines within the set. Our main contribution is a methodology for generating relevant bases able to tackle operational CSM. Experimental validation highlights that, for a given number of training samples, our set covering selection is a better strategy than selecting random pipelines or using all the available pipelines. Our analysis also shows that parameters as denoising, sharpening, and downsampling are very important to foster diversity. Finally, different benchmarks for classical and wild databases show the good generalization property of the extracted databases. Additional resources are available at github.com/RonyAbecidan/HolisticSteganalysisWithSetCovering

A Fully Dynamic Algorithm for k-Regret Minimizing Sets

Selecting a small set of representatives from a large database is important in many applications such as multi-criteria decision making, web search, and recommendation. The k-regret minimizing set (k-RMS) problem was recently proposed for representative tuple discovery. Specifically, for a large database P of tuples with multiple numerical attributes, the k-RMS problem returns a size-r subset Q of P such that, for any possible ranking function, the score of the top-ranked tuple in Q is not much worse than the score of the k th-ranked tuple in P. Although the k-RMS problem has been extensively studied in the literature, existing methods are designed for the static setting and cannot maintain the result efficiently when the database is updated. To address this issue, we propose the first fully-dynamic algorithm for the k-RMS problem that can efficiently provide the up-to-date result w.r.t. any tuple insertion and deletion in the database with a provable guarantee. Experimental results on several real-world and synthetic datasets demonstrate that our algorithm runs up to four orders of magnitude faster than existing k-RMS algorithms while providing results of nearly equal quality.Peer reviewe

Efficient Algorithms for k-Regret Minimizing Sets

A regret minimizing set Q is a small size representation of a much larger database P so that user queries executed on Q return answers whose scores are not much worse than those on the full dataset. In particular, a k-regret minimizing set has the property that the regret ratio between the score of the top-1 item in Q and the score of the top-k item in P is minimized, where the score of an item is the inner product of the item\u27s attributes with a user\u27s weight (preference) vector. The problem is challenging because we want to find a single representative set Q whose regret ratio is small with respect to all possible user weight vectors. We show that k-regret minimization is NP-Complete for all dimensions d>=3, settling an open problem from Chester et al. [VLDB 2014]. Our main algorithmic contributions are two approximation algorithms, both with provable guarantees, one based on coresets and another based on hitting sets. We perform extensive experimental evaluation of our algorithms, using both real-world and synthetic data, and compare their performance against the solution proposed in [VLDB 14]. The results show that our algorithms are significantly faster and scalable to much larger sets than the greedy algorithm of Chester et al. for comparable quality answers

Happiness Maximizing Sets under Group Fairness Constraints (Technical Report)

Finding a happiness maximizing set (HMS) from a database, i.e., selecting a small subset of tuples that preserves the best score with respect to any nonnegative linear utility function, is an important problem in multi-criteria decision-making. When an HMS is extracted from a set of individuals to assist data-driven algorithmic decisions such as hiring and admission, it is crucial to ensure that the HMS can fairly represent different groups of candidates without bias and discrimination. However, although the HMS problem was extensively studied in the database community, existing algorithms do not take group fairness into account and may provide solutions that under-represent some groups. In this paper, we propose and investigate a fair variant of HMS (FairHMS) that not only maximizes the minimum happiness ratio but also guarantees that the number of tuples chosen from each group falls within predefined lower and upper bounds. Similar to the vanilla HMS problem, we show that FairHMS is NP-hard in three and higher dimensions. Therefore, we first propose an exact interval cover-based algorithm called IntCov for FairHMS on two-dimensional databases. Then, we propose a bicriteria approximation algorithm called BiGreedy for FairHMS on multi-dimensional databases by transforming it into a submodular maximization problem under a matroid constraint. We also design an adaptive sampling strategy to improve the practical efficiency of BiGreedy. Extensive experiments on real-world and synthetic datasets confirm the efficacy and efficiency of our proposal.Comment: Technical report, a shorter version to appear in PVLDB 16(2