Social influence plays a vital role in shaping a user's behavior in online communities dealing with items of fine taste like movies, food, and beer. For online recommendation, this implies that users' preferences and ratings are influenced due to other individuals. Given only time-stamped reviews of users, can we find out who-influences-whom, and characteristics of the underlying influence network? Can we use this network to improve recommendation? While prior works in social-aware recommendation have leveraged social interaction by considering the observed social network of users, many communities like Amazon, Beeradvocate, and Ratebeer do not have explicit user-user links. Therefore, we propose GhostLink, an unsupervised probabilistic graphical model, to automatically learn the latent influence network underlying a review community -- given only the temporal traces (timestamps) of users' posts and their content. Based on extensive experiments with four real-world datasets with 13 million reviews, we show that GhostLink improves item recommendation by around 23% over state-of-the-art methods that do not consider this influence. As additional use-cases, we show that GhostLink can be used to differentiate between users' latent preferences and influenced ones, as well as to detect influential users based on the learned influence graph.