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Agricultural monitoring, especially in developing countries, can help prevent famine and support humanitarian efforts. A central challenge is yield estimation, i.e., predicting crop yields before harvest. We introduce a scalable, accurate, and inexpensive method to predict crop yields using publicly available remote sensing data. Our approach improves existing techniques in three ways. First, we forego hand-crafted features traditionally used in the remote sensing community and propose an approach based on modern representation learning ideas. We also introduce a novel dimensionality reduction technique that allows us to train a Convolutional Neural Network or Long-short Term Memory network and automatically learn useful features even when labeled training data are scarce. Finally, we incorporate a Gaussian Process component to explicitly model the spatio-temporal structure of the data and further improve accuracy. We evaluate our approach on county-level soybean yield prediction in the U.S. and show that it outperforms competing techniques.