Distribution-Free Conformal Joint Prediction Regions for Neural Marked Temporal Point Processes

Marked Temporal Point Processes (TPPs) are a valuable tool for modeling continuous-time event sequences and predicting the arrival time and type of future events. Neural TPPs leverage the expressive power of neural networks to address the limitations of classical TPP models, such as the Hawkes process, which are prone to misspecification errors due to their strong modeling assumptions. Quantifying uncertainty in these neural models, however, remains a significant challenge. Existing tools for uncertainty quantification often yield unreliable results, primarily because of implicit modeling assumptions and their dependence on asymptotic guarantees. This presentation will demonstrate how to construct well-calibrated, distribution-free neural TPP models from multiple event sequences using conformal prediction. Specifically, we will present methods to build a distribution-free joint prediction region for the event arrival time and type with a finite-sample coverage guarantee. We will first consider a naive but statistically valid approach that combines independent prediction regions for the event arrival time and type. By neglecting potential dependencies between these variables, this method can be overly conservative, resulting in large prediction regions. Then, we will introduce a more refined method based on the highest density regions, derived from the joint predictive density of event arrival time and type. This method effectively addresses the challenge of creating a joint prediction region for a bivariate response that includes both continuous and discrete data types. Additionally, we will assess the validity and efficiency of these methods through a comprehensive set of experiments on both simulated and real-world event sequence datasets.

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