Cryo-electron microscopy (cryoEM) is an increasingly popular method for protein structure determination. However, identifying a sufficient number of particles for analysis (often >100,000) can take months of manual effort. Current computational approaches are limited by high false positive rates and require significant ad-hoc post-processing, especially for unusually shaped particles. To address this shortcoming, we develop Topaz, an efficient and accurate particle picking pipeline using neural networks trained with few labeled particles by newly leveraging the remaining unlabeled particles through the framework of positive-unlabeled (PU) learning. Remarkably, despite using minimal labeled particles, Topaz allows us to improve reconstruction resolution by up to 0.15 {\AA} over published particles on three public cryoEM datasets without any post-processing. Furthermore, we show that our novel generalized-expectation criteria approach to PU learning outperforms existing general PU learning approaches when applied to particle detection, especially for challenging datasets of non-globular proteins. We expect Topaz to be an essential component of cryoEM analysis.