Inherent Trade-Offs in the Fair Determination of Risk Scores

Recent discussion in the public sphere about algorithmic classification has involved tension between competing notions of what it means for a probabilistic classification to be fair to different groups. We formalize three fairness conditions that lie at the heart of these debates, and we prove that except in highly constrained special cases, there is no method that can satisfy these three conditions simultaneously. Moreover, even satisfying all three conditions approximately requires that the data lie in an approximate version of one of the constrained special cases identified by our theorem. These results suggest some of the ways in which key notions of fairness are incompatible with each other, and hence provide a framework for thinking about the trade-offs between them.

Assessing Human Error Against a Benchmark of Perfection

An increasing number of domains are providing us with detailed trace data on human decisions in settings where we can evaluate the quality of these decisions via an algorithm. Motivated by this development, an emerging line of work has begun to consider whether we can characterize and predict the kinds of decisions where people are likely to make errors. To investigate what a general framework for human error prediction might look like, we focus on a model system with a rich history in the behavioral sciences: the decisions made by chess players as they select moves in a game. We carry out our analysis at a large scale, employing datasets with several million recorded games, and using chess tablebases to acquire a form of ground truth for a subset of chess positions that have been completely solved by computers but remain challenging even for the best players in the world. We organize our analysis around three categories of features that we argue are present in most settings where the analysis of human error is applicable: the skill of the decision-maker, the time available to make the decision, and the inherent difficulty of the decision. We identify rich structure in all three of these categories of features, and find strong evidence that in our domain, features describing the inherent difficulty of an instance are significantly more powerful than features based on skill or time.

Do Cascades Recur?

Cascades of information-sharing are a primary mechanism by which content reaches its audience on social media, and an active line of research has studied how such cascades, which form as content is reshared from person to person, develop and subside. In this paper, we perform a large-scale analysis of cascades on Facebook over significantly longer time scales, and find that a more complex picture emerges, in which many large cascades recur, exhibiting multiple bursts of popularity with periods of quiescence in between. We characterize recurrence by measuring the time elapsed between bursts, their overlap and proximity in the social network, and the diversity in the demographics of individuals participating in each peak. We discover that content virality, as revealed by its initial popularity, is a main driver of recurrence, with the availability of multiple copies of that content helping to spark new bursts. Still, beyond a certain popularity of content, the rate of recurrence drops as cascades start exhausting the population of interested individuals. We reproduce these observed patterns in a simple model of content recurrence simulated on a real social network. Using only characteristics of a cascade's initial burst, we demonstrate strong performance in predicting whether it will recur in the future.

Can Cascades be Predicted?

On many social networking web sites such as Facebook and Twitter, resharing or reposting functionality allows users to share others' content with their own friends or followers. As content is reshared from user to user, large cascades of reshares can form. While a growing body of research has focused on analyzing and characterizing such cascades, a recent, parallel line of work has argued that the future trajectory of a cascade may be inherently unpredictable. In this work, we develop a framework for addressing cascade prediction problems. On a large sample of photo reshare cascades on Facebook, we find strong performance in predicting whether a cascade will continue to grow in the future. We find that the relative growth of a cascade becomes more predictable as we observe more of its reshares, that temporal and structural features are key predictors of cascade size, and that initially, breadth, rather than depth in a cascade is a better indicator of larger cascades. This prediction performance is robust in the sense that multiple distinct classes of features all achieve similar performance. We also discover that temporal features are predictive of a cascade's eventual shape. Observing independent cascades of the same content, we find that while these cascades differ greatly in size, we are still able to predict which ends up the largest.

Engaging with Massive Online Courses

The Web has enabled one of the most visible recent developments in education---the deployment of massive open online courses. With their global reach and often staggering enrollments, MOOCs have the potential to become a major new mechanism for learning. Despite this early promise, however, MOOCs are still relatively unexplored and poorly understood. In a MOOC, each student's complete interaction with the course materials takes place on the Web, thus providing a record of learner activity of unprecedented scale and resolution. In this work, we use such trace data to develop a conceptual framework for understanding how users currently engage with MOOCs. We develop a taxonomy of individual behavior, examine the different behavioral patterns of high- and low-achieving students, and investigate how forum participation relates to other parts of the course. We also report on a large-scale deployment of badges as incentives for engagement in a MOOC, including randomized experiments in which the presentation of badges was varied across sub-populations. We find that making badges more salient produced increases in forum engagement.

You had me at hello: How phrasing affects memorability

Understanding the ways in which information achieves widespread public awareness is a research question of significant interest. We consider whether, and how, the way in which the information is phrased --- the choice of words and sentence structure --- can affect this process. To this end, we develop an analysis framework and build a corpus of movie quotes, annotated with memorability information, in which we are able to control for both the speaker and the setting of the quotes. We find that there are significant differences between memorable and non-memorable quotes in several key dimensions, even after controlling for situational and contextual factors. One is lexical distinctiveness: in aggregate, memorable quotes use less common word choices, but at the same time are built upon a scaffolding of common syntactic patterns. Another is that memorable quotes tend to be more general in ways that make them easy to apply in new contexts --- that is, more portable. We also show how the concept of "memorable language" can be extended across domains.

Echoes of power: Language effects and power differences in social interaction

Understanding social interaction within groups is key to analyzing online communities. Most current work focuses on structural properties: who talks to whom, and how such interactions form larger network structures. The interactions themselves, however, generally take place in the form of natural language --- either spoken or written --- and one could reasonably suppose that signals manifested in language might also provide information about roles, status, and other aspects of the group's dynamics. To date, however, finding such domain-independent language-based signals has been a challenge. Here, we show that in group discussions power differentials between participants are subtly revealed by how much one individual immediately echoes the linguistic style of the person they are responding to. Starting from this observation, we propose an analysis framework based on linguistic coordination that can be used to shed light on power relationships and that works consistently across multiple types of power --- including a more "static" form of power based on status differences, and a more "situational" form of power in which one individual experiences a type of dependence on another. Using this framework, we study how conversational behavior can reveal power relationships in two very different settings: discussions among Wikipedians and arguments before the U.S. Supreme Court.

The Directed Closure Process in Hybrid Social-Information Networks, with an Analysis of Link Formation on Twitter

It has often been taken as a working assumption that directed links in information networks are frequently formed by "short-cutting" a two-step path between the source and the destination -- a kind of implicit "link copying" analogous to the process of triadic closure in social networks. Despite the role of this assumption in theoretical models such as preferential attachment, it has received very little direct empirical investigation. Here we develop a formalization and methodology for studying this type of directed closure process, and we provide evidence for its important role in the formation of links on Twitter. We then analyze a sequence of models designed to capture the structural phenomena related to directed closure that we observe in the Twitter data.

Predicting Positive and Negative Links in Online Social Networks

We study online social networks in which relationships can be either positive (indicating relations such as friendship) or negative (indicating relations such as opposition or antagonism). Such a mix of positive and negative links arise in a variety of online settings; we study datasets from Epinions, Slashdot and Wikipedia. We find that the signs of links in the underlying social networks can be predicted with high accuracy, using models that generalize across this diverse range of sites. These models provide insight into some of the fundamental principles that drive the formation of signed links in networks, shedding light on theories of balance and status from social psychology; they also suggest social computing applications by which the attitude of one user toward another can be estimated from evidence provided by their relationships with other members of the surrounding social network.

Kronecker Graphs: An Approach to Modeling Networks

How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and densification and shrinking diameters over time. Most present network models either fail to match several of the above properties, are complicated to analyze mathematically, or both. In this paper we propose a generative model for networks that is both mathematically tractable and can generate networks that have the above mentioned properties. Our main idea is to use the Kronecker product to generate graphs that we refer to as "Kronecker graphs". First, we prove that Kronecker graphs naturally obey common network properties. We also provide empirical evidence showing that Kronecker graphs can effectively model the structure of real networks. We then present KronFit, a fast and scalable algorithm for fitting the Kronecker graph generation model to large real networks. A naive approach to fitting would take super- exponential time. In contrast, KronFit takes linear time, by exploiting the structure of Kronecker matrix multiplication and by using statistical simulation techniques. Experiments on large real and synthetic networks show that KronFit finds accurate parameters that indeed very well mimic the properties of target networks. Once fitted, the model parameters can be used to gain insights about the network structure, and the resulting synthetic graphs can be used for null- models, anonymization, extrapolations, and graph summarization.