Timely and high-resolution estimates of the home locations of a sufficiently large subset of the population are critical for effective disaster response and public health intervention, but this is still an open problem. Conventional data sources, such as census and surveys, have a substantial time lag and cannot capture seasonal trends. Recently, social media data has been exploited to address this problem by leveraging its large user-base and real-time nature. However, inherent sparsity and noise, along with large estimation uncertainty in home locations, have limited their effectiveness. Consequently, much of previous research has aimed only at a coarse spatial resolution, with accuracy being limited for high-resolution methods. In this paper, we develop a deep-learning solution that uses a two-phase dynamic structure to deal with sparse and noisy social media data. In the first phase, high recall is achieved using a random forest, producing more balanced home location candidates. Then two deep neural networks are used to detect home locations with high accuracy. We obtained over 90% accuracy for large subsets on a commonly used dataset. Compared to other high-resolution methods, our approach yields up to 60% error reduction by reducing high-resolution home prediction error from over 21% to less than 8%. Systematic comparisons show that our method gives the highest accuracy both for the entire sample and for subsets. Evaluation on a real-world public health problem further validates the effectiveness of our approach.