  In recent years, the field of recommendation systems has attracted increasing
attention to developing predictive models that provide explanations of why an
item is recommended to a user. The explanations can be either obtained by
post-hoc diagnostics after fitting a relatively complex model or embedded into
an intrinsically interpretable model. In this paper, we propose the explainable
recommendation systems based on a generalized additive model with manifest and
latent interactions (GAMMLI). This model architecture is intrinsically
interpretable, as it additively consists of the user and item main effects, the
manifest user-item interactions based on observed features, and the latent
interaction effects from residuals. Unlike conventional collaborative filtering
methods, the group effect of users and items are considered in GAMMLI. It is
beneficial for enhancing the model interpretability, and can also facilitate
the cold-start recommendation problem. A new Python package GAMMLI is developed
for efficient model training and visualized interpretation of the results. By
numerical experiments based on simulation data and real-world cases, the
proposed method is shown to have advantages in both predictive performance and
explainable recommendation.
