Proper Loss Functions for Nonlinear Hawkes Processes

Authors: Aditya Menon, Young Lee

AAAI 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We validate our theoretical analyses by illustrating the viability of using losses other than the standard maximum likelihood to fit various (non-)linear Hawkes processes.
Researcher Affiliation Academia Aditya Krishna Menon Data61 and the Australian National University aditya.menon@data61.csiro.au National University of Singapore dcsleey@nus.edu.sg
Pseudocode Yes Figure 1: Framework to fit nonlinear Hawkes processes. INPUT: Invertible nonlinearity F( ); kernels {ki}L i=1 PROCEDURE: (1) Construct canonical proper loss per Equation 24, or alternate loss with link per Equation 23 (2) Find the linear scorer that minimises 22 (3) Estimate intensity using Equation 18
Open Source Code No The paper does not provide concrete access to its own source code. It cites a third-party GitHub repository (Heusser 2013) which seems to contain the bitcoin dataset, not for the authors' own methodology.
Open Datasets Yes We compare the various losses on two real-world datasets: Last FM (Celma 2010), comprising the times that users listen to songs by artists... and bitcoin, comprising times of trades on the Mt Gox Bitcoin exchange for a single day (Heusser 2013).
Dataset Splits Yes For each dataset, we split the recorded event times into a train and test set. ... For Last FM, we select 500 random (user, artist) pairs for which there are at least 100 listening events over the span of at least two months. For each pair, we define the testing period to be the last month of the recorded history. For bitcoin, we use all trades occurring in the window 1PM 3PM for training, and make predictions in the window 3PM 4PM.
Hardware Specification No The paper does not provide specific hardware details used for running its experiments.
Software Dependencies No The paper does not provide specific software dependencies with version numbers. It only mentions the use of 'L-BFGS' for optimization.
Experiment Setup Yes We optimised the MLE and (modified) logistic loss with L-BFGS, enforcing a stationarity constraint that α < δ and a tolerance criterion of 10 8. For the logistic loss, we apply a weighting w = 108 on the background class, following Equation 28; for other losses, we set w = 1.