In many domain applications, a continuous timeline of human locations is critical; for example for understanding possible locations where a disease may spread, or the flow of traffic. While data sources such as GPS trackers or Call Data Records are temporally-rich, they are expensive, often not publicly available or garnered only in select locations, restricting their wide use. Conversely, geo-located social media data are publicly and freely available, but present challenges especially for full timeline inference due to their sparse nature. We propose a stochastic framework, Intermediate Location Computing (ILC) which uses prior knowledge about human mobility patterns to predict every missing location from an individual’s social media timeline. We compare ILC with a state-of-the-art RNN baseline as well as methods that are optimized for next-location prediction only. For three major cities, ILC predicts the top 1 location for all missing locations in a timeline, at 1 and 2-hour resolution, with up to 77.2% accuracy (up to 6% better accuracy than all compared methods). Specifically, ILC also outperforms the RNN in settings of low data; both cases of very small number of users (under 50), as well as settings with more users, but with sparser timelines. In general, the RNN model needs a higher number of users to achieve the same performance as ILC. Overall, this work illustrates the tradeoff between prior knowledge of heuristics and more data, for an important societal problem of filling in entire timelines using freely available, but sparse social media data.