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Diagnosing pain in neonates is difficult but critical. Although approximately thirty manual pain instruments have been developed for neonatal pain diagnosis, most are complex, multifactorial, and geared toward research. The goals of this work are twofold: 1) to develop a new video dataset for automatic neonatal pain detection called iCOPEvid (infant Classification Of Pain Expressions videos), and 2) to present a classification system that sets a challenging comparison performance on this dataset. The iCOPEvid dataset contains 234 videos of 49 neonates experiencing a set of noxious stimuli, a period of rest, and an acute pain stimulus. From these videos 20 s segments are extracted and grouped into two classes: pain (49) and nopain (185), with the nopain video segments handpicked to produce a highly challenging dataset. An ensemble of twelve global and local descriptors with a Bag-of-Features approach is utilized to improve the performance of some new descriptors based on Gaussian of Local Descriptors (GOLD). The basic classifier used in the ensembles is the Support Vector Machine, and decisions are combined by sum rule. These results are compared with standard methods, some deep learning approaches, and 185 human assessments. Our best machine learning methods are shown to outperform the human judges.