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

Scalable Audience Reach Estimation in Real-time Online Advertising

Online advertising has been introduced as one of the most efficient methods of advertising throughout the recent years. Yet, advertisers are concerned about the efficiency of their online advertising campaigns and consequently, would like to restrict their ad impressions to certain websites and/or certain groups of audience. These restrictions, known as targeting criteria, limit the reachability for better performance. This trade-off between reachability and performance illustrates a need for a forecasting system that can quickly predict/estimate (with good accuracy) this trade-off. Designing such a system is challenging due to (a) the huge amount of data to process, and, (b) the need for fast and accurate estimates. In this paper, we propose a distributed fault tolerant system that can generate such estimates fast with good accuracy. The main idea is to keep a small representative sample in memory across multiple machines and formulate the forecasting problem as queries against the sample. The key challenge is to find the best strata across the past data, perform multivariate stratified sampling while ensuring fuzzy fall-back to cover the small minorities. Our results show a significant improvement over the uniform and simple stratified sampling strategies which are currently widely used in the industry

Towards efficient SimRank computation on large networks

SimRank has been a powerful model for assessing the similarity of pairs of vertices in a graph. It is based on the concept that two vertices are similar if they are referenced by similar vertices. Due to its self-referentiality, fast SimRank computation on large graphs poses significant challenges. The state-of-the-art work [17] exploits partial sums memorization for computing SimRank in O(Kmn) time on a graph with n vertices and m edges, where K is the number of iterations. Partial sums memorizing can reduce repeated calculations by caching part of similarity summations for later reuse. However, we observe that computations among different partial sums may have duplicate redundancy. Besides, for a desired accuracy ϵ, the existing SimRank model requires K = [logC ϵ] iterations [17], where C is a damping factor. Nevertheless, such a geometric rate of convergence is slow in practice if a high accuracy is desirable. In this paper, we address these gaps. (1) We propose an adaptive clustering strategy to eliminate partial sums redundancy (i.e., duplicate computations occurring in partial sums), and devise an efficient algorithm for speeding up the computation of SimRank to 0(Kdn2) time, where d is typically much smaller than the average in-degree of a graph. (2) We also present a new notion of SimRank that is based on a differential equation and can be represented as an exponential sum of transition matrices, as opposed to the geometric sum of the conventional counterpart. This leads to a further speedup in the convergence rate of SimRank iterations. (3) Using real and synthetic data, we empirically verify that our approach of partial sums sharing outperforms the best known algorithm by up to one order of magnitude, and that our revised notion of SimRank further achieves a 5X speedup on large graphs while also fairly preserving the relative order of original SimRank scores