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Goal Recognition is the task of discerning the intended goal of an agent given a sequence of observations, whereas Plan Recognition consists of identifying the plan to achieve such intended goal. Regardless of the underlying techniques, most recognition approaches are directly affected by the quality of the available observations. In this paper, we develop neuro-symbolic recognition approaches that can combine learning and planning techniques, compensating for noise and missing observations using prior data. We evaluate our approaches in standard human-designed planning domains as well as domain models automatically learned from real-world data. Empirical experimentation shows that our approaches reliably infer goals and compute correct plans in the experimental datasets. An ablation study shows that outperform approaches that rely exclusively on the domain model, or exclusively on machine learning in problems with both noisy observations and low observability.