An important step in graph-based data analysis and processing is the construction of similarity graphs. Recent works have focused on the semi-supervised setting to learn an optimal similarity function for constructing a task-optimal graph. However, in many scenarios with billions of data points and trillions of potential edges, the run-time and computational requirements for training the similarity model make these approaches impractical. We present an efficient sampling approach by taking an adaptive partition view of locality sensitive hashing. Theoretically, we show that, though the samples obtained are correlated with sampling probabilities that do not sum to one, the training loss estimated for learning the graph similarity model using our approach is unbiased with a smaller variance compared to random sampling.