Abundant discordance among gene trees is widely documented, but the causes of this heterogeneity are varied. Discordance among estimated gene trees can stem from real sources such as coalescent processes, hybridization, and horizontal gene transfer (HGT). It can also stem from errors in data, such as hidden paralogy, mistaken homology, bad alignment, and contamination. While some of these processes create stochastic and subtle changes in gene tree topologies (e.g., human closer to gorilla than to chimp), others can produce unexpected patterns (e.g., guinea pig sister to gorilla). Given a large number of gene trees and a median species tree, one could attempt to automatically find these outliers among gene trees. In this paper, we develop a method that uses quartet-based subtree-prune-and-regraft (SPR) moves, paired with gradient-boosted decision trees, to predict whether parts of a gene tree disagree with species trees in unusual ways. We show that our method, GBOD, is quite accurate in finding HGT events, but less so in other scenarios. Nevertheless, this combination of machine learning and phylogenetic features provides a promising framework for outlier detection.