Nanopore sequencing platforms combined with supervised machine learning (ML) have been effective at detecting base modifications in DNA such as 5-methylcytosine (5mC) and N6-methyladenine (6mA). These ML-based nanopore callers have typically been trained on data that span all modifications on all possible DNA [Formula: see text]-mer backgrounds-a complete training dataset. However, as nanopore technology is pushed to more and more epigenetic modifications, such complete training data will not be feasible to obtain. Nanopore calling has historically been performed with hidden Markov models (HMMs) that cannot make successful calls for [Formula: see text]-mer contexts not seen during training because of their independent emission distributions. However, deep neural networks (DNNs), which share parameters across contexts, are increasingly being used as callers, often outperforming their HMM cousins. It stands to reason that a DNN approach should be able to better generalize to unseen [Formula: see text]-mer contexts. Indeed, herein we demonstrate that a common DNN approach (DeepSignal) outperforms a common HMM approach (Nanopolish) in the incomplete data setting. Furthermore, we propose a novel hybrid HMM-DNN approach, amortized-HMM, that outperforms both the pure HMM and DNN approaches on 5mC calling when the training data are incomplete. This type of approach is expected to be useful for calling other base modifications such as 5-hydroxymethylcytosine and for the simultaneous calling of different modifications, settings in which complete training data are not likely to be available.