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Maximizing the Spread of Influence Through a Social Network
 In KDD
, 2003
"... Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in gametheoretic settings, and the effects of ..."
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Cited by 963 (6 self)
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Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in gametheoretic settings, and the effects of “word of mouth ” in the promotion of new products. Recently, motivated by the design of viral marketing strategies, Domingos and Richardson posed a fundamental algorithmic problem for such social network processes: if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target? We consider this problem in several of the most widely studied models in social network analysis. The optimization problem of selecting the most influential nodes is NPhard here, and we provide the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63 % of optimal for several classes of models; our framework suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks. We also provide computational experiments on large collaboration networks, showing that in addition to their provable guarantees, our approximation algorithms significantly outperform nodeselection heuristics based on the wellstudied notions of degree centrality and distance centrality from the field of social networks.
Nearoptimal sensor placements in gaussian processes
 In ICML
, 2005
"... When monitoring spatial phenomena, which can often be modeled as Gaussian processes (GPs), choosing sensor locations is a fundamental task. There are several common strategies to address this task, for example, geometry or disk models, placing sensors at the points of highest entropy (variance) in t ..."
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Cited by 333 (34 self)
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When monitoring spatial phenomena, which can often be modeled as Gaussian processes (GPs), choosing sensor locations is a fundamental task. There are several common strategies to address this task, for example, geometry or disk models, placing sensors at the points of highest entropy (variance) in the GP model, and A, D, or Eoptimal design. In this paper, we tackle the combinatorial optimization problem of maximizing the mutual information between the chosen locations and the locations which are not selected. We prove that the problem of finding the configuration that maximizes mutual information is NPcomplete. To address this issue, we describe a polynomialtime approximation that is within (1 − 1/e) of the optimum by exploiting the submodularity of mutual information. We also show how submodularity can be used to obtain online bounds, and design branch and bound search procedures. We then extend our algorithm to exploit lazy evaluations and local structure in the GP, yielding significant speedups. We also extend our approach to find placements which are robust against node failures and uncertainties in the model. These extensions are again associated with rigorous theoretical approximation guarantees, exploiting the submodularity of the objective function. We demonstrate the advantages of our approach towards optimizing mutual information in a very extensive empirical study on two realworld data sets.
Active learning literature survey
, 2010
"... The key idea behind active learning is that a machine learning algorithm can achieve greater accuracy with fewer labeled training instances if it is allowed to choose the data from which is learns. An active learner may ask queries in the form of unlabeled instances to be labeled by an oracle (e.g., ..."
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Cited by 311 (1 self)
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The key idea behind active learning is that a machine learning algorithm can achieve greater accuracy with fewer labeled training instances if it is allowed to choose the data from which is learns. An active learner may ask queries in the form of unlabeled instances to be labeled by an oracle (e.g., a human annotator). Active learning is wellmotivated in many modern machine learning problems, where unlabeled data may be abundant but labels are difficult, timeconsuming, or expensive to obtain. This report provides a general introduction to active learning and a survey of the literature. This includes a discussion of the scenarios in which queries can be formulated, and an overview of the query strategy frameworks proposed in the literature to date. An analysis of the empirical and theoretical evidence for active learning, a summary of several problem setting variants, and a discussion
Diversifying Search Results
, 2009
"... We study the problem of answering ambiguous web queries in a setting where there exists a taxonomy of information, and that both queries and documents may belong to more than one category according to this taxonomy. We present a systematic approach to diversifying results that aims to minimize the r ..."
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Cited by 276 (5 self)
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We study the problem of answering ambiguous web queries in a setting where there exists a taxonomy of information, and that both queries and documents may belong to more than one category according to this taxonomy. We present a systematic approach to diversifying results that aims to minimize the risk of dissatisfaction of the average user. We propose an algorithm that well approximates this objective in general, and is provably optimal for a natural special case. Furthermore, we generalize several classical IR metrics, including NDCG, MRR, and MAP, to explicitly account for the value of diversification. We demonstrate empirically that our algorithm scores higher in these generalized metrics compared to results produced by commercial search engines.
Combinatorial Auctions with Decreasing Marginal Utilities
, 2001
"... This paper considers combinatorial auctions among such submodular buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross s ..."
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Cited by 207 (25 self)
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This paper considers combinatorial auctions among such submodular buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross substitutes property. Those last valuations are shown to form a zeromeasure subset of the submodular valuations that have positive measure. While we show that the allocation problem among submodular valuations is NPhard, we present an efficient greedy 2approximation algorithm for this case and generalize it to the case of limited complementarities. No such approximation algorithm exists in a setting allowing for arbitrary complementarities. Some results about strategic aspects of combinatorial auctions among players with decreasing marginal utilities are also presented.
PseudoBoolean Optimization
 DISCRETE APPLIED MATHEMATICS
, 2001
"... This survey examines the state of the art of a variety of problems related to pseudoBoolean optimization, i.e. to the optimization of set functions represented by closed algebraic expressions. The main parts of the survey examine general pseudoBoolean optimization, the specially important case of ..."
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Cited by 183 (5 self)
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This survey examines the state of the art of a variety of problems related to pseudoBoolean optimization, i.e. to the optimization of set functions represented by closed algebraic expressions. The main parts of the survey examine general pseudoBoolean optimization, the specially important case of quadratic pseudoBoolean optimization (to which every pseudoBoolean optimization can be reduced), several other important special classes, and approximation algorithms.
Scalable Influence Maximization for Prevalent Viral Marketing in LargeScale Social Networks
"... Influence maximization, defined by Kempe, Kleinberg, and Tardos (2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models. The scalability of influence maximization is a key factor for enabling preval ..."
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Cited by 173 (13 self)
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Influence maximization, defined by Kempe, Kleinberg, and Tardos (2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models. The scalability of influence maximization is a key factor for enabling prevalent viral marketing in largescale online social networks. Prior solutions, such as the greedy algorithm of Kempe et al. (2003) and its improvements are slow and not scalable, while other heuristic algorithms do not provide consistently good performance on influence spreads. In this paper, we design a new heuristic algorithm that is easily scalable to millions of nodes and edges in our experiments. Our algorithm has a simple tunable parameter for users to control the balance between the running time and the influence spread of the algorithm. Our results from extensive simulations on several realworld and synthetic networks demonstrate that our algorithm is currently the best scalable solution to the influence maximization problem: (a) our algorithm scales beyond millionsized graphs where the greedy algorithm becomes infeasible, and (b) in all size ranges, our algorithm performs consistently well in influence spread — it is always among the best algorithms, and in most cases it significantly outperforms all other scalable heuristics to as much as 100%–260 % increase in influence spread.
Algorithms in Discrete Convex Analysis
 Math. Programming
, 2000
"... this paper is to describe the f#eA damental results on M and Lconvex f#24L2A+ with special emphasis on algorithmic aspects. ..."
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Cited by 161 (34 self)
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this paper is to describe the f#eA damental results on M and Lconvex f#24L2A+ with special emphasis on algorithmic aspects.
Influential Nodes in a Diffusion Model for Social Networks
 IN ICALP
, 2005
"... We study the problem of maximizing the expected spread of an innovation or behavior within a social network, in the presence of "wordofmouth" referral. Our work builds on the observation that individuals' decisions to purchase a product or adopt an innovation are strongly influe ..."
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Cited by 153 (3 self)
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We study the problem of maximizing the expected spread of an innovation or behavior within a social network, in the presence of "wordofmouth" referral. Our work builds on the observation that individuals' decisions to purchase a product or adopt an innovation are strongly influenced by recommendations from their friends and acquaintances. Understanding