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In physical layer authentication (PLA) mechanisms, a verifier decides whether a received message has been transmitted by a legitimate user or an intruder, according to some features of the physical channel over which the message traveled. To design the authentication check implemented at the verifier, typically either the statistics or a dataset of features are available for the channel from the legitimate user, while no information is available when under attack. When the statistics are known, a well-known good solution is the likelihood test (LT). When a dataset is available, the decision problem is one-class classification (OCC) and a good understanding of the machine learning (ML) techniques used for its solution is important to ensure security. Thus, in this paper, we aim at obtaining ML PLA verifiers that operate as the LT. We show how to do it with the neural network (NN) and the one-class least-squares support vector machine (OCLSSVM) models, trained as two-class classifiers on the single-class dataset and an artificial dataset. The artificial dataset for the negative class is obtained by generating channel feature (CF) vectors uniformly distributed over the domain of the legitimate class dataset. We also derive a modified stochastic gradient descent (SGD) algorithm that trains a PLA verifier operating as LT without the need for the artificial dataset. Furthermore, we show that the one-class least-squares support vector machine with suitable kernels operates as the LT at convergence. Lastly, we show that the widely used autoencoder classifier generally does not provide the LT. Numerical results are provided considering PLA on both wireless and underwater acoustic channels.