Detecting anomalies in dynamic rating data: a robust probabilistic model for rating evolution

Rating data is ubiquitous on websites such as Amazon, TripAdvisor, or Yelp. Since ratings are not static but given at various points in time, a temporal analysis of rating data provides deeper insights into the evolution of a product's quality. In this work, we tackle the following question: Given the time stamped rating data for a product or service, how can we detect the general rating behavior of users as well as time intervals where the ratings behave anomalous? We propose a Bayesian model that represents the rating data as sequence of categorical mixture models. In contrast to existing methods, our method does not require any aggregation of the input but it operates on the original time stamped data. To capture the dynamic effects of the ratings, the categorical mixtures are temporally constrained: Anomalies can occur in specific time intervals only and the general rating behavior should evolve smoothly over time. Our method automatically determines the intervals where anomalies occur, and it captures the temporal effects of the general behavior by using a state space model on the natural parameters of the categorical distributions. For learning our model, we propose an efficient algorithm combining principles from variational inference and dynamic programming. In our experimental study we show the effectiveness of our method and we present interesting discoveries on multiple real world datasets.