Cognitive assessment is a growing area in psychological and educational measurement, where tests are given to assess mastery/deficiency of attributes or skills. A key issue is the correct identification of attributes associated with items in a test. In this paper, we set up a mathematical framework under which theoretical properties may be discussed. We establish sufficient conditions to ensure that the attributes required by each item are learnable from the data.
"Theory of self-learning $Q$-matrix." Bernoulli 19 (5A) 1790 - 1817, November 2013. https://doi.org/10.3150/12-BEJ430