A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to plate diagrams for directed graphical models. To exploit efficient tensor algebra in graphs with plates of variables, we generalize undirected factor graphs to plated factor graphs and variable elimination to a tensor variable elimination algorithm that operates directly on plated factor graphs. Moreover, we generalize complexity bounds based on treewidth and characterize the class of plated factor graphs for which inference is tractable. As an application, we integrate tensor variable elimination into the Pyro probabilistic programming language to enable exact inference in discrete latent variable models with repeated structure. We validate our methods with experiments on both directed and undirected graphical models, including applications to polyphonic music modeling, animal movement modeling, and latent sentiment analysis.

Pyro is a probabilistic programming language built on Python as a platform for developing advanced probabilistic models in AI research. To scale to large data sets and high-dimensional models, Pyro uses stochastic variational inference algorithms and probability distributions built on top of PyTorch, a modern GPU-accelerated deep learning framework. To accommodate complex or model-specific algorithmic behavior, Pyro leverages Poutine, a library of composable building blocks for modifying the behavior of probabilistic programs.

e-Commerce has many core problems which can benefit from data mining-constructing recommendations for users, designing product taxonomies in a way that the user finds easy to navigate to, facility allocation for inventory to minimize shipping costs-to name a few. A big component of e-commerce data comprises of search activity. Search as a share of traffic has overtaken direct browsing, and most e-commerce sites generate more search data than browse data. Search session data is also more voluminous than any user aggregated data since it includes anonymous sessions. However, search data is inherently local to a query. Therefore, it is not immediately obvious whether it can be used to build global (i.e., where no query is involved) knowledge to address many of these problems that are of interest. In this paper, we introduce a global structure, namely islands of interest, that is mined from local search data. We show that these concentrations of user search intent are highly relevant to each of the e-commerce problems mentioned earlier. We introduce two algorithms-one based on community detection, and the other on clustering-that can identify islands of interest. We build a framework that can compare the characteristics of the islands identified using these two approaches. We believe that in addition to providing insights into user behavior, islands of interest can be important in tackling lesser researched problems such as the design of product taxonomies.

Groupon is a major e-commerce company. It is unique in the sense that it is not only a vendor of goods, but also of local deals (such as restaurants, spas, activities, etc.) that reflect various aspects of a user's interests. In this sense, Groupon has a complete view of its users' lifestyle preferences. This is different from e-commerce goods vendors, who, for instance, may not have direct insight into what restaurants are preferred by their users, or what nightlife they prefer. We may say that Groupon engages the entire "lifestyle persona" of its users. Motivated by this, we consider the large scale problem of mining such "lifestyle personas" from Groupon's activity data collected over 38 million e-commerce users. This includes users drawn from one of the world's largest mobile user bases. Our solution combines domain knowledge from e-commerce with data mining and graph theoretic methods. Since Groupon offers deals and goods across the 360 degree gamut of user preferences, do lifestyle personas in its data also span this gamut? What are some of the significant personas that emerge from this data mining? Are the differences between personas gross or subtle? These are some of the questions we answer conclusively in our study. Our mined personas are both descriptive and distinctive, and offer insights into customer behaviors and lifestyles. Our work is being used to redesign the user experience, as well as to power product recommendations at Groupon.

Customer Relationship Management (CRM) is currently the fastest growing sector of enterprise software, estimated to increase to $36.5B worldwide by 2017. CRM technologies increasingly use data mining primitives across multiple applications. At the same time, the growth of big data has led to the evolution of an open source big data software stack (primarily powered by Apache software) that rivals traditional enterprise database (RDBMS) stacks. New technologies such as Kafka, Storm, HBase have significantly enriched this open source stack, alongside more established technologies such as Hadoop MapReduce and Mahout. Today, enterprises have a choice to make regarding which stack they will choose to power their big data applications. However, there are no published studies in literature on enterprise big data pipelines built using open source components supporting CRM. Specific questions that enterprises have include: how is the data processed and analyzed in such pipelines? What are the building blocks of such pipelines? How long does each step of this processing take? In this work, we answer these questions for a large scale (serving over a 100M customers) industrial CRM pipeline that incorporates data mining, and serves several applications. Our pipeline has, broadly, two parts. The first is a data gathering part that uses Kafka, Storm, and HBase. The second is a data mining part that uses Mahout and Hadoop MapReduce. We also provide timings for common tasks in the second part such as data preprocessing for machine learning, clustering, reservoir sampling, and frequent itemset extraction.

Understanding how specific, ambiguous, or broad the intent of a search query is, across all users of the system, is important in improving search relevance in eCommerce. There is scant literature on such a structural characterization of queries in eCommerce. In this paper, we use query-click log data to address the problem of identifying "atypical queries": these are queries that are extremal in terms of specificity, ambiguity, or breadth of intent. We isolate three components of atypicality: geometric, statistical, and topological. We demonstrate, using query-click logs at Groupon, that certain combinations of these properties render a query atypical, and discuss how search analysts treat such queries differently. Our work is being used to improve search relevance at Groupon.