Discovering Topical Interactions in Text-Based Cascades Using Hidden Markov Hawkes Processes

Abstract

Social media conversations unfold based on complex interactions between users, topics and time. While recent models have been proposed to capture network strengths between users, users' topical preferences and temporal patterns between posting and response times, interaction patterns between topics has not been studied. We argue that social media conversations naturally involve interacting rather than independent topics. Modeling such topical interaction patterns can additionally help in inference of latent variables in the data such as diffusion parents and topics of events. We propose the Hidden Markov Hawkes Process (HMHP) that incorporates topical Markov Chains within Hawkes processes to jointly model topical interactions along with useruser and user-topic patterns. We propose a Gibbs sampling algorithm for HMHP that jointly infers the network strengths, diffusion paths, the topics of the posts as well as the topictopic interactions. We show using experiments on real and semisynthetic data that HMHP is able to generalize better and recover the network strengths, topics and diffusion paths more accurately that state-of-the-art baselines. More interestingly, HMHP finds insightful interactions between topics in real tweets which no existing model is able to do. This can potentially lead to actionable insights enabling, e.g., user targeting for influence maximization.

Bayesian estimation of decay parameters in Hawkes processes

“…While baseline and jump parameters of Hawkes processes are typically derived via convex optimization, the estimation of decay parameters in exponential kernels remains an open issue. Previous work simply assumed the decay parameters to be constants [3,12,18], cross-validated decay parameter values [11,17,39], or estimated them with a range of different optimization approaches [4,13,19,29,35,40,48]. Such estimation approaches result in point estimates that can be considered as sufficient for simulating and predicting event streams.…”

Hawkes Process Classification through Discriminative Modeling of Text

“…[34] focusses on the problem of inferring the diffusion of information together with the topics characterizing the information using Hawkes process and topic modeling. Another work related to topic modeling is [35] where authors have proposed Hidden Markov Hawkes Process that incorporates topical Markov Chains within Hawkes processes to jointly model topical interactions along with user-user and user-topic patterns. [36] has used the combination of Dirichlet process and Hawkes process for clustering document streams.…”

Surfacing Estimation Uncertainty in the Decay Parameters of Hawkes Processes with Exponential Kernels

“…Previous work suggested a wide range of methods to address the decay estimation problem with approaches that provide point estimates. These approaches include setting β to a given constant value [5], [8], [9], cross-validation over a range of values [1], [10], [11], or the application of a general optimization method. Those methods comprise non-linear optimization [12], [13], Bayesian hyperparameter optimization [16], [17], expectation-maximization [15], [32] or visual inspection of the log-likelihood function [6], [14].…”

“…While baseline and jump parameters of Hawkes processes are typically derived via convex optimization, the estimation of decay parameters in exponential kernels remains an open issue. Previous work simply assumed the decay parameters to be constants [5], [8], [9], cross-validated decay parameter values [1], [10], [11], or estimated them with a range of different optimization approaches [6], [12]- [17]. Such estimation approaches result in point estimates that can be considered as sufficient for simulating and predicting event streams.…”