Discovering Latent Network Structure in Point Process Data (1402.0914v1)

Abstract: Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or impossible to measure the network directly. Examples of latent networks include economic interactions linking financial instruments and patterns of reciprocity in gang violence. In these cases, we are limited to noisy observations of events associated with each node. To enable analysis of these implicit networks, we develop a probabilistic model that combines mutually-exciting point processes with random graph models. We show how the Poisson superposition principle enables an elegant auxiliary variable formulation and a fully-Bayesian, parallel inference algorithm. We evaluate this new model empirically on several datasets.

• The paper introduces a novel probabilistic approach using Hawkes processes and random graph priors to reveal hidden network structures within point process data.
• The paper demonstrates significant improvements in predictive accuracy, particularly in financial and social systems, through advanced Bayesian inference techniques.
• The paper highlights practical applications by modeling short-term market interactions and uncovering spatial-temporal dynamics in complex social scenarios.

Discovering Latent Network Structure in Point Process Data

The paper under review investigates the analysis of latent network structures within point process data, which is especially relevant in domains where direct measurements of network interactions are impractical. Common examples include the financial markets and cybersecurity realms where interactions within economic instruments or between entities engaged in illicit activities yield insight into underlying structures. The authors focus on modeling these implicit networks through a probabilistic lens by integrating mutually-exciting point processes with random graph methodologies.

Central to their approach is the utilization of the Hawkes process, which enables the modeling of event-based data that innately contains temporal interdependencies. The paper articulates how the Poisson superposition principle elegantly facilitates the decomposition of these processes, thereby allowing for effective Bayesian inference. This formulation supports not only the development of efficient inference algorithms but also allows for the incorporation of complexity in network models through exchangeable random graph priors.

The proposed model shines in scenarios such as those involving financial markets, where trades in related industries may be suitably captured by spikes that propagate through a latent network. Empirical efficacy is evidenced by evaluations over datasets that typify these complex environments. Strong numerical assertions are made in terms of predictive accuracy, particularly in the application to S&P 100 stock price changes where significant background rate variations and short-term interactions are taken into account through flexible components like the Log Gaussian Cox Process. The model demonstrates improvements in predictive log likelihoods as compared to baseline Hawkes models when applied to these financial datasets.

In the domain of social systems, specifically gang-related violence in Chicago, the model performs well in unveiling latent social structures that govern observed incidents of violence. The paper underscores the importance of considering both spatial and temporal elements in such datasets and leverages a variety of graph models to enhance the interpretability of emerging patterns. The research concludes that novel graph models such as Erdős-Renyi graph priors in tandem with network clustering offer superior performance metrics in terms of predictive capacity, highlighting certain network configurations that align with historical socio-police datasets.

The implications of this research span both theoretical and practical facets. Theoretically, it presents an advanced formulation whereby latent network structure can be embedded within point process frameworks. Practically, it opens new avenues to explore complex systems where latent interactions are key and connects seemingly disparate events through the discovery of coherent interdependencies.

Looking forward, the approach holds promise in more advanced AI applications. Future research may extend these paradigms by incorporating non-linear and non-stationary dynamics in the latent network inference process. Additionally, scaling this framework to accommodate real-time data streams would pivotally enhance its applicability in dynamic environments such as online financial trading platforms or adaptive cybersecurity monitoring systems.

In summary, the paper offers a comprehensive methodology to uncover latent networks in event-driven data, demonstrating significant improvements in understanding and modeling implicitly connected systems. This work sets a robust foundation for subsequent research within the latent network discovery field, illustrating critical advancements in probabilistic modeling and inference within point process contexts.