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.

Optimizing relevance and revenue in ad search

We provide several new results related to the concept of min-wise independence Our main result is that any randomized sampling scheme for the relative intersection of sets based on testing equality of samples yields an equivalent min-wise independent family Thus, in a certain sense, min-wise independent families are complete for this type of estimation We also discuss the notion of robustness, a concept extending min-wise independence to allow more efficient use of it in practice A surprising result arising from our consideration of robustness is that under a random permutation from a min-wise independent family, any element of a fixed set has an equal chance to get any rank in the image of the set, not only the minimum as required by definition

Completeness and Robustness Properties of Min-Wise Independent Permutations

Machine generated business-to-consumer (B2C) emails such as receipts, newsletters, and promotions constitute a large portion of users’ inboxes today. These emails reflect the users’ interests and often are sequentially correlated, e.g., users interested in relocating may receive a sequence of messages on housing, moving, job availability, etc. We aim to infer (and eventually serve) the users’ future interests by predicting the categories of their future emails. There are many useful methods, such as recurrent neural networks, that can be applied for such predictions, but in all cases the key to better performance is an effective representation of emails and users. To this end, we propose a general framework for learning embeddings for emails and users, using as input only the sequence of B2C templates users receive and open. (A template is a B2C email stripped of all transient information related to specific users.) These learned embeddings allow us to identify both sequentially correlated emails and users with similar sequential interests. We can also use the learned embeddings either as input features or embedding initializers for email category prediction tasks. Extensive experiments with millions of fully anonymized B2C emails demonstrate that the learned embeddings can significantly improve the prediction accuracy for future email categories. We hope that this effective yet simple embedding learning framework will inspire new machine intelligence applications that will improve the users’ email experience.

Learning Effective Embeddings for Machine Generated Emails with Applications to Email Category Prediction

The classic IR model assumes a human engaged in activity that generates an "information need". This need is verbalized and then expressed as a query to search engine over a defined corpus. In the past decade, Web search engines have evolved from a first generation based on classic IR algorithms scaled to web size and thus supporting only informational queries, to a second generation supporting navigational queries using web specific information (primarily link analysis), to a third generation enabling transactional and other "semantic" queries based on a variety of technologies aimed to directly satisfy the unexpressed "user intent", thus moving further and further away from the classic model.

What is coming next? In this talk, we identify two trends, both representing "short-circuits" of the model: The first is the trend towards context driven Information Supply (IS), that is, the goal of Web IR will widen to include the supply of relevant information from multiple sources without requiring the user to make an explicit query. The information supply concept greatly precedes information retrieval; what is new in the web framework, is the ability to supply relevant information specific to a given activity and a given user, while the activity is being performed. Thus the entire verbalization and query-formation phase are eliminated. The second trend is "social search" driven by the fact that the Web has evolved to being simultaneously a huge repository of knowledge and a vast social environment. As such, it is often more effective to ask the members of a given web milieu rather than construct elaborate queries. This short-circuits only the query formulation, but allows information finding activities such as opinion elicitation and discovery of social norms, that are not expressible at all as queries against a fixed corpus.

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The next generation web search and the demise of the classic IR model

Back in the heady days of 1999 and WWW8 (Toronto) we held a panel titled "Finding Anything in the Billion Page Web: Are Algorithms the Key?" In retrospect the answer to this question seems laughably obvious - the search industry has burgeoned on a foundation of algorithms, cloud computing and machine learning. As we move into the second decade of this millennium, we are confronted with a dizzying array of new paradigms for finding content, including social networks and location-based search and advertising. This panel pulls together senior experts from academia and the major search principals to debate whether search will continue to look anything like the 2-keywords-give-10-blue-links paradigm that Google has popularized. What do emerging approaches and paradigms - natural language search, social search, location-based search - mean for the future of search in general?

Andrei Z. Broder

Papers

Optimizing relevance and revenue in ad search

Completeness and Robustness Properties of Min-Wise Independent Permutations

Learning Effective Embeddings for Machine Generated Emails with Applications to Email Category Prediction

The next generation web search and the demise of the classic IR model

Search is dead!: long live search