Multi-way Interacting Regression via Factorization Machines
This work addresses the challenge of interaction selection in regression for domains like genetics and retail, but it appears incremental as it builds on existing factorization and prior models.
The authors tackled the problem of modeling multi-way interactions among predictor variables in regression by proposing a Bayesian method using factorization and hypergraph priors, achieving the ability to identify meaningful interactions in genetics and retail demand forecasting.
We propose a Bayesian regression method that accounts for multi-way interactions of arbitrary orders among the predictor variables. Our model makes use of a factorization mechanism for representing the regression coefficients of interactions among the predictors, while the interaction selection is guided by a prior distribution on random hypergraphs, a construction which generalizes the Finite Feature Model. We present a posterior inference algorithm based on Gibbs sampling, and establish posterior consistency of our regression model. Our method is evaluated with extensive experiments on simulated data and demonstrated to be able to identify meaningful interactions in applications in genetics and retail demand forecasting.