The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. 
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. 
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. 
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

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Statistical mechanics of complex networks

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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The Structure and Function of Complex Networks

A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known—a collaboration network and a food web—and find that it detects significant and informative community divisions in both cases.

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Community structure in social and biological networks

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.

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Finding and evaluating community structure in networks.

How much can an imperfect source of randomness affect an algorithm? We examine several simple questions of this type concerning the long-term behavior of a random walk on a finite graph. In our setup, at each step of the random walk a “controller” can, with a certain small probability, fix the next step, thus introducing a bias. We analyze the extent to which the bias can affect the limit behavior of the walk. The controller is assumed to associate a real, nonnegative, “benefit” with each state, and to strive to maximize the long-term expected benefit. We derive tight bounds on the maximum of this objective function over all controller's strategies, and present polynomial time algorithms for computing the optimal controller strategy.

Biased random walks

Methods and systems for presenting content such as articles based on utility are provided. In one embodiment, a plurality of articles are determined, each article in the plurality of articles including article content and a corresponding preview icon, the preview icon defining a link to the corresponding article content when presented. For each article in the plurality of articles, a user experience utility value is determined. And for each article in the plurality of articles, an economic utility value is also determined. A ranked order of the articles is determined based upon each article's user experience utility value and economic utility value. And a portion of the preview icons of the articles are presented on a graphical display page in a priority orientation based on the ranked order of the articles.

Presentation of Content Based on Utility

Methods and systems are provided that may be used to determine a probability of whether a visitor to a web document is likely to click on a web advertisement. An exemplary method may include detecting one or more features in a web document. One or more expert statistical models to which the web document belongs may be determined and associated weightings may be determined based, at least in part, on the one or more features detected. A click-through-rate probability for a web advertisement to be placed on the web document may be estimated based on the one or more expert statistical models.

Method and system for quantifying user interactions with web advertisements

Sponsored search is a three-way interaction between advertisers, users, and the search engine. The basic ad selection in sponsored search, lets the advertiser choose the exact queries where the ad is to be shown. To increase advertising volume, many advertisers opt into advanced match, where the search engine can select additional queries that are deemed relevant for the advertiser's ad. In advanced match, the search engine is effectively bidding on the behalf of the advertisers. While advanced match has been extensively studied in the literature from the ad relevance perspective there is little work that discusses how to infer the appropriate bid value for a given advanced match. The bid value is crucial as it affects both the ad placement in revenue reordering and the amount advertisers are charged in case of a click.We propose a statistical approach to solve the bid generation problem and examine two information sources: the bidding behavior of advertisers, and the conversion data. Our key finding suggests that sophisticated advertisers' bids are driven by many factors beyond clicks and immediate measurable conversions, likely capturing the value chain of an ad display ranging from views, clicks, profit margins, etc., representing the total ROI from the advertising.

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Bid generation for advanced match in sponsored search

Methods for selecting one or more advertisements based on previously captured relevance data to serve to a client system requesting a primary webpage is provided. The client displays a referring webpage having a hyperlink to the primary webpage. Upon selection of the hyperlink, the client sends a request to a content server storing the primary webpage. The content server classifies the primary webpage for content and retrieves persistent relevance information, possibly including a referrer of the primary webpage comprising a URL address of the referring webpage, a listing of other recently visited webpages, a listing of any bid phrases from previously displayed advertisements, and a listing of recent click data. The content server sends the primary webpage to the client, which includes an advertisement server request. The transaction between the content server and the advertisement server includes persistence relevance information to select advertisements to serve to the client.

Andrei Z. Broder

Papers

Biased random walks

Presentation of Content Based on Utility

Method and system for quantifying user interactions with web advertisements

Bid generation for advanced match in sponsored search

System and method for retargeting advertisements based on previously captured relevance data