We introduce Aggregation Queries over Nearest Neighbors (AQNNs), a novel type of aggregation queries over the predicted neighborhood of a designated object. AQNNs are prevalent in modern applications where, for instance, a medical professional may want to compute "the average systolic blood pressure of patients whose predicted condition is similar to a given insomnia patient". Since prediction typically involves an expensive deep learning model or a human expert, we formulate query processing as the problem of returning an approximate aggregate by combining an expensive oracle and a cheaper model (e.g, a simple ML model) to compute the predictions. We design the Sampler with Precision-Recall in Target (SPRinT) framework for answering AQNNs. SPRinT consists of sampling, nearest neighbor refinement, and aggregation, and is tailored for various aggregation functions. It enjoys provable theoretical guarantees, including bounds on sample size and on error in approximate aggregates. Our extensive experiments on medical, e-commerce, and video datasets demonstrate that SPRinT consistently achieves the lowest aggregation error with minimal computation cost compared to its baselines. Scalability results show that SPRinT's execution time and aggregation error remain stable as the dataset size increases, confirming its suitability for large-scale applications.