Bayesian method speeds up event intensity estimation for large data
Martingale Posterior Cox Processes
Machine Learning
Summary
Modeling events that happen over time can be hard because the methods can be slow and complex. The authors present a new way to estimate how often events occur that avoids complicated assumptions and runs much faster on modern computer hardware. Their method looks at the events themselves instead of hidden layers, making it easier to understand. Tests show this approach works well on both made-up and real-world data while using fewer computing resources.
What this means in practice
- •For real-time data engineers: Estimate event intensities in streaming applications more efficiently without complex model tuning.
- •For financial risk analysts: Model event-driven risks faster for large transaction datasets to improve decision times.
Authors
Joshua Rooijakkers, Edwin Fong
Abstract
Cox processes provide a principled Bayesian nonparametric framework for modeling event-based data through an underlying intensity function. However, existing inference methods for estimating the intensity typically rely on computationally expensive Markov chain Monte Carlo sampling or approximate inference techniques. In addition, to ensure tractability, these methods often define priors over indirect latent structures, making them challenging to interpret. In this paper, we introduce the Martingale Posterior Cox Process (MPCP), which recasts Bayesian intensity estimation as inference over unobserved events given the observed event history. This perspective avoids the need to define complex priors while retaining the flexibility of nonparametric modeling. We propose a scalable, GPU-friendly copula-based predictive update, and provide strong theoretical guarantees for the convergence of the predictive resampling algorithm. Empirically, we show that MPCP provides excellent performance in both simulations and real data at a fraction of the computational cost of competing Bayesian approaches.