  Various factorization-based methods have been proposed to leverage
second-order, or higher-order cross features for boosting the performance of
predictive models. They generally enumerate all the cross features under a
predefined maximum order, and then identify useful feature interactions through
model training, which suffer from two drawbacks. First, they have to make a
trade-off between the expressiveness of higher-order cross features and the
computational cost, resulting in suboptimal predictions. Second, enumerating
all the cross features, including irrelevant ones, may introduce noisy feature
combinations that degrade model performance. In this work, we propose the
Adaptive Factorization Network (AFN), a new model that learns arbitrary-order
cross features adaptively from data. The core of AFN is a logarithmic
transformation layer to convert the power of each feature in a feature
combination into the coefficient to be learned. The experimental results on
four real datasets demonstrate the superior predictive performance of AFN
against the start-of-the-arts.
