Variational Inference for Sparse Gaussian Process Modulated Hawkes Process

The Hawkes process (HP) has been widely applied to modeling self-exciting events including neuron spikes, earthquakes and tweets. To avoid designing parametric triggering kernel and to be able to quantify the prediction confidence, the non-parametric Bayesian HP has been proposed. However, the inference of such models suffers from unscalability or slow convergence. In this paper, we aim to solve both problems. Specifically, first, we propose a new non-parametric Bayesian HP in which the triggering kernel is modeled as a squared sparse Gaussian process. Then, we propose a novel variational inference schema for model optimization. We employ the branching structure of the HP so that maximization of evidence lower bound (ELBO) is tractable by the expectation-maximization algorithm. We propose a tighter ELBO which improves the fitting performance. Further, we accelerate the novel variational inference schema to linear time complexity by leveraging the stationarity of the triggering kernel. Different from prior acceleration methods, ours enjoys higher efficiency. Finally, we exploit synthetic data and two large social media datasets to evaluate our method. We show that our approach outperforms state-of-the-art non-parametric frequentist and Bayesian methods. We validate the efficiency of our accelerated variational inference schema and practical utility of our tighter ELBO for model selection. We observe that the tighter ELBO exceeds the common one in model selection

Event Uncertainty using Ensemble Neural Hawkes Process

Various real world applications in science and industry are often recorded over time as asynchronous event sequences. These event sequences comprise of the time of occurrence of events. Different applications including such event sequences are crime analysis, earthquake prediction, neural spiking train study, infectious disease prediction etc. A principled framework for modeling asynchronous event sequences is temporal point process. Recent works on neural temporal point process have combined the theoretical foundation of point process with universal approximation ability of neural networks. However, the predictions made by these models are uncertain due to incorrect model inference. Therefore, it is highly desirable to associate uncertainty with the predictions as well. In this paper, we propose a novel model, Ensemble Neural Hawkes Process, which is capable of predicting event occurrence time along with uncertainty, hence improving the generalization capability. We also propose evaluation metric which captures the uncertainty modelling capability for event prediction. The efficacy of proposed model is demonstrated using various simulated and real world datasets

Variational Bayesian Inference for Nonlinear Hawkes Process with Gaussian Process Self-Effects

Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results.DFG, 318763901, SFB 1294: Datenassimilation – Die nahtlose Verschmelzung von Daten und ModellenBMBF, 01IS18025A, Verbundprojekt BIFOLD-BBDC: Berlin Institute for the Foundations of Learning and DataBMBF, 01IS18037A, Verbundprojekt BIFOLD-BZML: Berlin Institute for the Foundations of Learning and Dat

30th International Conference on Information Modelling and Knowledge Bases

Information modelling is becoming more and more important topic for researchers, designers, and users of information systems. The amount and complexity of information itself, the number of abstraction levels of information, and the size of databases and knowledge bases are continuously growing. Conceptual modelling is one of the sub-areas of information modelling. The aim of this conference is to bring together experts from different areas of computer science and other disciplines, who have a common interest in understanding and solving problems on information modelling and knowledge bases, as well as applying the results of research to practice. We also aim to recognize and study new areas on modelling and knowledge bases to which more attention should be paid. Therefore philosophy and logic, cognitive science, knowledge management, linguistics and management science are relevant areas, too. In the conference, there will be three categories of presentations, i.e. full papers, short papers and position papers

Variational inference for sparse gaussian process modulated hawkes process

The Hawkes process (HP) has been widely applied to modeling self-exciting events including neuron spikes, earthquakes and tweets. To avoid designing parametric triggering kernel and to be able to quantify the prediction confidence, the nonparametric Bayesian HP has been proposed. However, the inference of such models suffers from unscalability or slow convergence. In this paper, we aim to solve both problems. Specifically, first, we propose a new non-parametric Bayesian HP in which the triggering kernel is modeled as a squared sparse Gaussian process. Then, we propose a novel variational inference schema for model optimization. We employ the branching structure of the HP so that maximization of evidence lower bound (ELBO) is tractable by the expectation-maximization algorithm. We propose a tighter ELBO which improves the fitting performance. Further, we accelerate the novel variational inference schema to linear time complexity by leveraging the stationarity of the triggering kernel. Different from prior acceleration methods, ours enjoys higher efficiency. Finally, we exploit synthetic data and two large social media datasets to evaluate our method. We show that our approach outperforms state-of-the-art non-parametric frequentist and Bayesian methods. We validate the efficiency of our accelerated variational inference schema and practical utility of our tighter ELBO for model selection. We observe that the tighter ELBO exceeds the common one in model selection