Scalable Continuous-time Diffusion Framework for Network Inference and Influence Estimation

TL;DR

The paper tackles inferring diffusion networks and estimating seed-set influence from continuous-time cascades when the underlying network is unknown, addressing severe scalability gaps in prior methods. It introduces a scalable continuous-time framework (FIM) based on a continuous-time dynamical system and a small-time-step approximation, along with a sampling-based technique (SDTS) to accelerate influence estimation. The authors provide theoretical analysis of the approximation error and its impact on influence estimates, and demonstrate through extensive experiments on real and synthetic data that FIM achieves superior accuracy and scales to networks with tens of thousands of nodes, outperforming baselines in both network inference and influence estimation tasks. The approach offers practical impact for large-scale diffusion analysis, enabling efficient learning from cascades and fast estimation of propagation potential in real-world networks.

Abstract

The study of continuous-time information diffusion has been an important area of research for many applications in recent years. When only the diffusion traces (cascades) are accessible, cascade-based network inference and influence estimation are two essential problems to explore. Alas, existing methods exhibit limited capability to infer and process networks with more than a few thousand nodes, suffering from scalability issues. In this paper, we view the diffusion process as a continuous-time dynamical system, based on which we establish a continuous-time diffusion model. Subsequently, we instantiate the model to a scalable and effective framework (FIM) to approximate the diffusion propagation from available cascades, thereby inferring the underlying network structure. Furthermore, we undertake an analysis of the approximation error of FIM for network inference. To achieve the desired scalability for influence estimation, we devise an advanced sampling technique and significantly boost the efficiency. We also quantify the effect of the approximation error on influence estimation theoretically. Experimental results showcase the effectiveness and superior scalability of FIM on network inference and influence estimation.

Figures (11)

• Figure 1: Diffusion function $p(2,t)$.
• Figure 2: Illustration of a diffusion cascade.
• Figure 3: Running time on HR.
• Figure 4: Running time on Meme.
• Figure 5: Running time on synthetic datasets.

Theorems & Definitions (12)

• Definition 1: Network Inference
• Definition 2: Influence Estimation
• Lemma 1
• Lemma 2
• Definition 3: Continuous-time Dynamical System katok1997introductionbrin2002introduction
• Definition 4: Continuous-time Diffusion Propagation
• Theorem 1
• Theorem 2
• Definition 5: Shortest Diffusion Time of Set
• Lemma 3