  Estimation of the large $Q$-matrix in Cognitive Diagnosis Models (CDMs) with
many items and latent attributes from observational data has been a huge
challenge due to its high computational cost. Borrowing ideas from deep
learning literature, we propose to learn the large $Q$-matrix by Restricted
Boltzmann Machines (RBMs) to overcome the computational difficulties. In this
paper, key relationships between RBMs and CDMs are identified. Consistent and
robust learning of the $Q$-matrix in various CDMs is shown to be valid under
certain conditions. Our simulation studies under different CDM settings show
that RBMs not only outperform the existing methods in terms of learning speed,
but also maintain good recovery accuracy of the $Q$-matrix. In the end, we
illustrate the applicability and effectiveness of our method through a real
data analysis on the Cattell's 16 personality test data set.
