Multi-output Polynomial Networks and Factorization Machines
This work addresses multi-class and multi-task learning problems, offering an incremental improvement by adapting existing models to handle multiple outputs more efficiently.
The paper tackles the problem of extending factorization machines and polynomial networks to multi-output settings for learning vector-valued functions, achieving excellent accuracy with sparser models on classification tasks and outperforming baselines in ranking accuracy on recommendation systems.
Factorization machines and polynomial networks are supervised polynomial models based on an efficient low-rank decomposition. We extend these models to the multi-output setting, i.e., for learning vector-valued functions, with application to multi-class or multi-task problems. We cast this as the problem of learning a 3-way tensor whose slices share a common basis and propose a convex formulation of that problem. We then develop an efficient conditional gradient algorithm and prove its global convergence, despite the fact that it involves a non-convex basis selection step. On classification tasks, we show that our algorithm achieves excellent accuracy with much sparser models than existing methods. On recommendation system tasks, we show how to combine our algorithm with a reduction from ordinal regression to multi-output classification and show that the resulting algorithm outperforms simple baselines in terms of ranking accuracy.