Superposition-Assisted Stochastic Optimization for Hawkes Processes
This work addresses the cold-start problem in sequential recommendation systems, though it appears incremental as it builds on existing Hawkes process models with a novel superposition strategy.
The authors tackled the problem of learning multi-agent Hawkes processes by proposing a stochastic optimization algorithm with a diversity-driven superposition strategy, which improved risk bounds and convergence properties, achieving better learning results on synthetic data and demonstrating potential for cold-start recommendation systems on real-world data.
We consider the learning of multi-agent Hawkes processes, a model containing multiple Hawkes processes with shared endogenous impact functions and different exogenous intensities. In the framework of stochastic maximum likelihood estimation, we explore the associated risk bound. Further, we consider the superposition of Hawkes processes within the model, and demonstrate that under certain conditions such an operation is beneficial for tightening the risk bound. Accordingly, we propose a stochastic optimization algorithm assisted with a diversity-driven superposition strategy, achieving better learning results with improved convergence properties. The effectiveness of the proposed method is verified on synthetic data, and its potential to solve the cold-start problem of sequential recommendation systems is demonstrated on real-world data.