We present $\textbf{$\texttt{SkillQG}$}$: a question generation framework with controllable comprehension types for assessing and improving machine reading comprehension models. Existing question generation systems widely differentiate questions by $\textit{literal}$ information such as question words and answer types to generate semantically relevant questions for a given context. However, they rarely consider the $\textit{comprehension}$ nature of questions, i.e. the different comprehension capabilities embodied by different questions. In comparison, our $\texttt{SkillQG}$ is able to tailor a fine-grained assessment and improvement to the capabilities of question answering models built on it. Specifically, we first frame the comprehension type of questions based on a hierarchical skill-based schema, then formulate $\texttt{SkillQG}$ as a skill-conditioned question generator. Furthermore, to improve the controllability of generation, we augment the input text with question focus and skill-specific knowledge, which are constructed by iteratively prompting the pre-trained language models. Empirical results demonstrate that $\texttt{SkillQG}$ outperforms baselines in terms of quality, relevance, and skill-controllability while showing a promising performance boost in downstream question answering task.
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