In-region location verification (IRLV) aims at verifying whether a user is inside a region of interest (ROI). In wireless networks, IRLV can exploit the features of the channel between the user and a set of trusted access points. In practice, the channel feature statistics is not available and we resort to machine learning (ML) solutions for IRLV. We first show that solutions based on either neural networks (NNs) or support vector machines (SVMs) and typical loss functions are Neyman-Pearson (N-P)-optimal at learning convergence for sufficiently complex learning machines and large training datasets . Indeed, for finite training, ML solutions are more accurate than the N-P test based on estimated channel statistics. Then, as estimating channel features outside the ROI may be difficult, we consider one-class classifiers, namely auto-encoders NNs and one-class SVMs, which however are not equivalent to the generalized likelihood ratio test (GLRT), typically replacing the N-P test in the one-class problem. Numerical results support the results in realistic wireless networks, with channel models including path-loss, shadowing, and fading.