User experience in social media involves rich interactions with the media content and other participants in the community. In order to support such communities, it is important to understand the factors that drive the users' engagement. In this paper we show how to define statistical models of different complexity to describe patterns of song listening in an online music community. First, we adapt the LDA model to capture music taste from listening activities across users and identify both the groups of songs associated with the specific taste and the groups of listeners who share the same taste. Second, we define a graphical model that takes into account listening sessions and captures the listening moods of users in the community. Our session model leads to groups of songs and groups of listeners with similar behavior across listening sessions and enables faster inference when compared to the LDA model. Our experiments with the data from an online media site demonstrate that the session model is better in terms of the perplexity compared to two other models: the LDA-based taste model that does not incorporate cross-session information and a baseline model that does not use latent groupings of songs.

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.