From Competition to Complementarity: Comparative Influence Diffusion and Maximization

Influence maximization is a well-studied problem that asks for a small set of influential users from a social network, such that by targeting them as early adopters, the expected total adoption through influence cascades over the network is maximized. However, almost all prior work focuses on cascades of a single propagating entity or purely-competitive entities. In this work, we propose the Comparative Independent Cascade (Com-IC) model that covers the full spectrum of entity interactions from competition to complementarity. In Com-IC, users' adoption decisions depend not only on edge-level information propagation, but also on a node-level automaton whose behavior is governed by a set of model parameters, enabling our model to capture not only competition, but also complementarity, to any possible degree. We study two natural optimization problems, Self Influence Maximization and Complementary Influence Maximization, in a novel setting with complementary entities. Both problems are NP-hard, and we devise efficient and effective approximation algorithms via non-trivial techniques based on reverse-reachable sets and a novel "sandwich approximation". The applicability of both techniques extends beyond our model and problems. Our experiments show that the proposed algorithms consistently outperform intuitive baselines in four real-world social networks, often by a significant margin. In addition, we learn model parameters from real user action logs.Comment: An abridged of this work is to appear in the Proceedings of VLDB Endowment (PVDLB), Vol 9, No 2. Also, the paper will be presented in the VLDB 2016 conference in New Delhi, India. This update contains new theoretical and experimental results, and the paper is now in single-column format (44 pages

Influence Maximization with Bandits

We consider the problem of \emph{influence maximization}, the problem of maximizing the number of people that become aware of a product by finding the `best' set of `seed' users to expose the product to. Most prior work on this topic assumes that we know the probability of each user influencing each other user, or we have data that lets us estimate these influences. However, this information is typically not initially available or is difficult to obtain. To avoid this assumption, we adopt a combinatorial multi-armed bandit paradigm that estimates the influence probabilities as we sequentially try different seed sets. We establish bounds on the performance of this procedure under the existing edge-level feedback as well as a novel and more realistic node-level feedback. Beyond our theoretical results, we describe a practical implementation and experimentally demonstrate its efficiency and effectiveness on four real datasets.Comment: 12 page

Validating Network Value of Influencers by means of Explanations

Recently, there has been significant interest in social influence analysis. One of the central problems in this area is the problem of identifying influencers, such that by convincing these users to perform a certain action (like buying a new product), a large number of other users get influenced to follow the action. The client of such an application is a marketer who would target these influencers for marketing a given new product, say by providing free samples or discounts. It is natural that before committing resources for targeting an influencer the marketer would be interested in validating the influence (or network value) of influencers returned. This requires digging deeper into such analytical questions as: who are their followers, on what actions (or products) they are influential, etc. However, the current approaches to identifying influencers largely work as a black box in this respect. The goal of this paper is to open up the black box, address these questions and provide informative and crisp explanations for validating the network value of influencers. We formulate the problem of providing explanations (called PROXI) as a discrete optimization problem of feature selection. We show that PROXI is not only NP-hard to solve exactly, it is NP-hard to approximate within any reasonable factor. Nevertheless, we show interesting properties of the objective function and develop an intuitive greedy heuristic. We perform detailed experimental analysis on two real world datasets - Twitter and Flixster, and show that our approach is useful in generating concise and insightful explanations of the influence distribution of users and that our greedy algorithm is effective and efficient with respect to several baselines

Show Me the Money: Dynamic Recommendations for Revenue Maximization

Recommender Systems (RS) play a vital role in applications such as e-commerce and on-demand content streaming. Research on RS has mainly focused on the customer perspective, i.e., accurate prediction of user preferences and maximization of user utilities. As a result, most existing techniques are not explicitly built for revenue maximization, the primary business goal of enterprises. In this work, we explore and exploit a novel connection between RS and the profitability of a business. As recommendations can be seen as an information channel between a business and its customers, it is interesting and important to investigate how to make strategic dynamic recommendations leading to maximum possible revenue. To this end, we propose a novel \model that takes into account a variety of factors including prices, valuations, saturation effects, and competition amongst products. Under this model, we study the problem of finding revenue-maximizing recommendation strategies over a finite time horizon. We show that this problem is NP-hard, but approximation guarantees can be obtained for a slightly relaxed version, by establishing an elegant connection to matroid theory. Given the prohibitively high complexity of the approximation algorithm, we also design intelligent heuristics for the original problem. Finally, we conduct extensive experiments on two real and synthetic datasets and demonstrate the efficiency, scalability, and effectiveness our algorithms, and that they significantly outperform several intuitive baselines.Comment: Conference version published in PVLDB 7(14). To be presented in the VLDB Conference 2015, in Hawaii. This version gives a detailed submodularity proo