Field-Embedded Factorization Machines for Click-through rate prediction

Click-through rate (CTR) prediction models are common in many online applications such as digital advertising and recommender systems. Field-Aware Factorization Machine (FFM) and Field-weighted Factorization Machine (FwFM) are state-of-the-art among the shallow models for CTR prediction. Recently, many deep learning-based models have also been proposed. Among deeper models, DeepFM, xDeepFM, AutoInt+, and FiBiNet are state-of-the-art models. The deeper models combine a core architectural component, which learns explicit feature interactions, with a deep neural network (DNN) component. We propose a novel shallow Field-Embedded Factorization Machine (FEFM) and its deep counterpart Deep Field-Embedded Factorization Machine (DeepFEFM). FEFM learns symmetric matrix embeddings for each field pair along with the usual single vector embeddings for each feature. FEFM has significantly lower model complexity than FFM and roughly the same complexity as FwFM. FEFM also has insightful mathematical properties about important fields and field interactions. DeepFEFM combines the FEFM interaction vectors learned by the FEFM component with a DNN and is thus able to learn higher order interactions. We conducted comprehensive experiments over a wide range of hyperparameters on two large publicly available real-world datasets. When comparing test AUC and log loss, the results show that FEFM and DeepFEFM outperform the existing state-of-the-art shallow and deep models for CTR prediction tasks. We have made the code of FEFM and DeepFEFM available in the DeepCTR library (https://github.com/shenweichen/DeepCTR).