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Noisy, intermediate-scale quantum (NISQ) computing devices have become an industrial reality in the last few years, and cloud-based interfaces to these devices are enabling exploration of near-term quantum computing on a range of problems. As NISQ devices are too noisy for many of the algorithms with a known quantum advantage, discovering impactful applications for near-term devices is the subject of intense research interest. We explore quantum-assisted machine learning (QAML) on NISQ devices through the perspective of tensor networks (TNs), which offer a robust platform for designing resource-efficient and expressive machine learning models to be dispatched on quantum devices. In particular, we lay out a framework for designing and optimizing TN-based QAML models using classical techniques, and then compiling these models to be run on quantum hardware, with demonstrations for generative matrix product state (MPS) models. We put forth a generalized canonical form for MPS models that aids in compilation to quantum devices, and demonstrate greedy heuristics for compiling with a given topology and gate set that outperforms known generic methods in terms of the number of entangling gates, e.g., CNOTs, in some cases by an order of magnitude. We present an exactly solvable benchmark problem for assessing the performance of MPS QAML models, and also present an application for the canonical MNIST handwritten digit dataset. The impacts of hardware topology and day-to-day experimental noise fluctuations on model performance are explored by analyzing both raw experimental counts and statistical divergences of inferred distributions. We also present parametric studies of depolarization and readout noise impacts on model performance using hardware simulators.