Hidden Markov models (HMMs) are frequently used in areas such as speech recognition and bioinformatics. However, implementing HMM algorithms correctly and efficiently is time-consuming and error-prone. Specifically, using model-specific knowledge to improve performance, such as sparsity in the transition probability matrix, ties the implementation to a particular model, making it harder to modify. Previous work has introduced high-level frameworks for defining HMMs, thus lifting the burden of efficiently implementing HMM algorithms from the user. However, existing tools are ill-suited for sparse HMMs with many states. This paper introduces Trellis, a domain-specific language for succinctly defining sparse HMMs that use GPU acceleration to achieve high performance. We show that Trellis outperforms previous work and is on par with a hand-written CUDA kernel implementation for a particular sparse HMM.