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.
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