We present half-life regression (HLR), a novel model for spaced repetition practice with applications to second language acquisition.HLR combines psycholinguistic theory with modern machine learning techniques, indirectly estimating the "halflife" of a word or concept in a student's long-term memory.We use data from Duolingo -a popular online language learning application -to fit HLR models, reducing error by 45%+ compared to several baselines at predicting student recall rates.HLR model weights also shed light on which linguistic concepts are systematically challenging for second language learners.Finally, HLR was able to improve Duolingo daily student engagement by 12% in an operational user study.

Given a graph with billions of nodes and edges, how can we find patterns and anomalies? Are there nodes that participate in too many or too few triangles? Are there close-knit near-cliques? These questions are expensive to answer unless we have the first several eigenvalues and eigenvectors of the graph adjacency matrix. However, eigensolvers suffer from subtle problems (e.g., convergence) for large sparse matrices, let alone for billion-scale ones. We address this problem with the proposed HEIGEN algorithm, which we carefully design to be accurate, efficient, and able to run on the highly scalable MAPREDUCE (HADOOP) environment. This enables HEIGEN to handle matrices more than 1;000 × larger than those which can be analyzed by existing algorithms. We implement HEIGEN and run it on the M45 cluster, one of the top 50 supercomputers in the world. We report important discoveries about nearcliques and triangles on several real-world graphs, including a snapshot of the Twitter social network (56 Gb, 2 billion edges) and the “YahooWeb” data set, one of the largest publicly available graphs (120 Gb, 1.4 billion nodes, 6.6 billion edges).

Given a graph with node attributes, how can we find meaningful patterns such as clusters, bridges, and outliers? Attributed graphs appear in real world in the form of social networks with user interests, gene interaction networks with gene expression information, phone call networks with customer demographics, and many others. In effect, we want to group the nodes into clusters with similar connectivity and homogeneous attributes. Most existing graph clustering algorithms either consider only the connectivity structure of the graph and ignore the node attributes, or require several user-defined parameters such as the number of clusters. We propose PICS, a novel, parameter-free method for mining attributed graphs. Two key advantages of our method are that (1) it requires no user-specified parameters such as the number of clusters and similarity functions, and (2) its running time scales linearly with total graph and attribute size. Our experiments show that PICS reveals meaningful and insightful patterns and outliers in both synthetic and real datasets, including call networks, political books, political blogs, and collections from Twitter and YouTube which have more than 70K nodes and 30K attributes.

Understanding a network's temporal evolution appears to require multiple observations of the graph over time. These often expensive repeated crawls are only able to answer questions about what happened from observation to observation, and not what happened before or between network snapshots. Contrary to this picture, we propose a method for Twitter's social network that takes a single static snapshot of network edges and user account creation times to accurately infer when these edges were formed. This method can be exact in theory, and we demonstrate empirically for a large subset of Twitter relationships that it is accurate to within a few hours in practice.

There is a widespread intuitive sense that different kinds of information spread differently on-line, but it has been difficult to evaluate this question quantitatively since it requires a setting where many different kinds of information spread in a shared environment. Here we study this issue on Twitter, analyzing the ways in which tokens known as hashtags spread on a network defined by the interactions among Twitter users. We find significant variation in the ways that widely-used hashtags on different topics spread.