Amit Goyal

Learning influence probabilities in social networks

Recently, there has been tremendous interest in the phenomenon of influence propagation in social networks. The studies in this area assume they have as input to their problems a social graph with edges labeled with probabilities of influence between users. However, the question of where these probabilities come from or how they can be computed from real social network data has been largely ignored until now. Thus it is interesting to ask whether from a social graph and a log of actions by its users, one can build models of influence. This is the main problem attacked in this paper. In addition to proposing models and algorithms for learning the model parameters and for testing the learned models to make predictions, we also develop techniques for predicting the time by which a user may be expected to perform an action. We validate our ideas and techniques using the Flickr data set consisting of a social graph with 1.3M nodes, 40M edges, and an action log consisting of 35M tuples referring to 300K distinct actions. Beyond showing that there is genuine influence happening in a real social network, we show that our techniques have excellent prediction performance.

CELF++: optimizing the greedy algorithm for influence maximization in social networks

Kempe et al. [4] (KKT) showed the problem of influence maximization is NP-hard and a simple greedy algorithm guarantees the best possible approximation factor in PTIME. However, it has two major sources of inefficiency. First, finding the expected spread of a node set is #P-hard. Second, the basic greedy algorithm is quadratic in the number of nodes. The first source is tackled by estimating the spread using Monte Carlo simulation or by using heuristics[4, 6, 2, 5, 1, 3]. Leskovec et al. proposed the CELF algorithm for tackling the second. In this work, we propose CELF++ and empirically show that it is 35-55% faster than CELF.

A data-based approach to social influence maximization

Influence maximization is the problem of finding a set of users in a social network, such that by targeting this set, one maximizes the expected spread of influence in the network. Most of the literature on this topic has focused exclusively on the social graph, overlooking historical data, i.e., traces of past action propagations. In this paper, we study influence maximization from a novel data-based perspective. In particular, we introduce a new model, which we call credit distribution, that directly leverages available propagation traces to learn how influence flows in the network and uses this to estimate expected influence spread. Our approach also learns the different levels of influence-ability of users, and it is time-aware in the sense that it takes the temporal nature of influence into account. We show that influence maximization under the credit distribution model is NP-hard and that the function that defines expected spread under our model is submodular. Based on these, we develop an approximation algorithm for solving the influence maximization problem that at once enjoys high accuracy compared to the standard approach, while being several orders of magnitude faster and more scalable.

SIMPATH: An Efficient Algorithm for Influence Maximization under the Linear Threshold Model

There is significant current interest in the problem of influence maximization: given a directed social network with influence weights on edges and a number k, find k seed nodes such that activating them leads to the maximum expected number of activated nodes, according to a propagation model. Kempe et al. showed, among other things, that under the Linear Threshold Model, the problem is NP-hard, and that a simple greedy algorithm guarantees the best possible approximation factor in PTIME. However, this algorithm suffers from various major performance drawbacks. In this paper, we propose Simpath, an efficient and effective algorithm for influence maximization under the linear threshold model that addresses these drawbacks by incorporating several clever optimizations. Through a comprehensive performance study on four real data sets, we show that Simpath consistently outperforms the state of the art w.r.t. running time, memory consumption and the quality of the seed set chosen, measured in terms of expected influence spread achieved.

Maximizing product adoption in social networks

One of the key objectives of viral marketing is to identify a small set of users in a social network, who when convinced to adopt a product will influence others in the network leading to a large number of adoptions in an expected sense. The seminal work of Kempe et al. [13] approaches this as the problem of influence maximization. This and other previous papers tacitly assume that a user who is influenced (or, informed) about a product necessarily adopts the product and encourages her friends to adopt it. However, an influenced user may not adopt the product herself, and yet form an opinion based on the experiences of her friends, and share this opinion with others. Furthermore, a user who adopts the product may not like the product and hence not encourage her friends to adopt it to the same extent as another user who adopted and liked the product. This is independent of the extent to which those friends are influenced by her. Previous works do not account for these phenomena. We argue that it is important to distinguish product adoption from influence. We propose a model that factors in a users experience (or projected experience) with a product. We adapt the classical Linear Threshold (LT) propagation model by defining an objective function that explicitly captures product adoption, as opposed to influence. We show that under our model, adoption maximization is NP-hard and the objective function is monotone and submodular, thus admitting an approximation algorithm. We perform experiments on three real popular social networks and show that our model is able to distinguish between influence and adoption, and predict product adoption much more accurately than approaches based on the classical LT model.

GuruMine: A Pattern Mining System for Discovering Leaders and Tribes

In this demo we introduce GuruMine, a pattern mining system for the discovery of leaders, i.e., influential users in social networks, and their tribes, i.e., a set of users usually influenced by the same leader over several actions. GuruMine is built upon a novel pattern mining framework for leaders discovery, that we introduced in [1]. In particular, we consider social networks where users perform actions. Actions may be as simple as tagging resources (urls) as in del.icio.us, rating songs as in Yahoo! Music, or movies as in Yahoo! Movies, or users buying gadgets such as cameras, handholds, etc. and blogging a review on the gadgets. The assumption is that actions performed by a user can be seen by their network friends. Users seeing their friends actions are sometimes tempted to perform those actions. On the basis of the propagation of such influence, in [1] we provided various notion of leaders and developed algorithms for their efficient discovery. GuruMine provides users with a friendly graphical interface for selecting the actions of interest, and the kind of leaders to mine. The set of parameters driving the pattern discovery process can be iteratively refined, and the result is updated, if possible without incurring a completely new computation. Once a set of leaders has been extracted, GuruMine can easily validate them on a set of actions unseen during the pattern mining, by analyzing the portion of network reached by the influence of the selected leaders on the unseen actions. GuruMine also offers various visualizations over the social networks: the propagation of an action, the leaders, their tribes, and the interactions between different leaders and tribes. In this demo we will show: (i) how the pattern mining process can be driven towards the discovery of a good set of leaders, (ii) the ease of use of GuruMine system, and (iii) its outstanding performances on large real-world social networks and actions databases.

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 essentially 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.