Title: Efficient Multivariate Temporal Point Process via Monotone Alternating Splines
Primary area: learning on time series and dynamical systems
Keywords: Temporal Point Process, Cumulative Conditional Intensity Function, Monotone Splines

Abstract: Temporal point processes (TPPs) have widespread applications across various domains. Compared to modeling the conditional intensity of a TPP, modeling its conditional cumulative intensity function (CCIF) improves efficiency and eliminates approximation error. However, currently, the parametrization of CCIF remains limited and scarce. This paper proposes a novel method called the Monotone Alternating Spline (MAS). By leveraging two distinct interpolation and extrapolation components, MAS provides a broad framework for modeling CCIF, offering greater flexibility and efficiency. Theoretically, MAS's interpolation grants a strong fitting ability, while its extrapolation guarantees robust generalization. Extensive experiments illuminate that MAS achieves state-of-the-art performance on both synthetic and real-world datasets.