We propose a non-parametric link prediction algorithm for a sequence of graph snapshots over time. The model predicts links based on the features of its endpoints, as well as those of the local neighborhood around the endpoints. This allows for different types of neighborhoods in a graph, each with its own dynamics (e.g, growing or shrinking communities). We prove the consistency of our estimator, and give a fast implementation based on locality-sensitive hashing. Experiments with simulated as well as five real-world dynamic graphs show that we outperform the state of the art, especially when sharp fluctuations or non-linearities are present.