  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).
