Network Recovery from Cascade Data: A Debiased Jacobian-Based Machine Learning Approach

2026-06-05

AI Summary

This study addresses the problem of model-free recovery of latent influence networks from observed cascade data. To this end, the authors propose CascadeNet, a framework that characterizes influence structures by nonparametrically estimating the Jacobian matrix of the one-step transition function and constructs a Neyman-orthogonal debiased estimator via the Riesz representation theorem, enabling √n-consistent and asymptotically normal inference for network edges. The method makes no assumptions about the underlying diffusion mechanism and achieves state-of-the-art accuracy in network recovery across nine simulation scenarios. In an empirical application to COVID-19 transmission across Spain’s 52 provinces, the inferred network exhibits strong alignment with actual human mobility patterns and significantly outperforms existing baselines.

Abstract

Many important outcomes unfold as dynamic cascades, including product adoption, disease spread, financial distress, and information diffusion. A central challenge is to recover the hidden influence network behind these cascades. Existing methods typically assume a specific diffusion model, and their performance degrades substantially when that assumption is misspecified. We propose CascadeNet, a Jacobian-based machine learning framework for network recovery that does not require specifying a diffusion mechanism. The key idea is that the underlying influence structure can be characterized by the Jacobian of the one-step transition function. CascadeNet first constructs a flexible estimator of the transition function, and further applies Neyman-orthogonal debiasing via the Riesz representer, so that the debiased Jacobian is $\sqrt{n}$-consistent and asymptotically normal, enabling formal inference on the network structure. We validate CascadeNet in both a simulation exercise and a real-world empirical application. In simulations, where the data-generating process is known, CascadeNet achieves the highest network recovery accuracy across nine common data-generating processes. In an empirical application to COVID-19 transmission across Spain's 52 provinces, CascadeNet recovers transmission networks that are significantly correlated with the true inter-province mobility network, whereas networks recovered by baseline methods show no significant alignment with the ground truth.

Problem

• network recovery
• cascade data
• influence network
• diffusion model
• hidden structure

Innovation

• Jacobian-based inference
• network recovery
• debiased machine learning
• cascade data
• Neyman-orthogonal debiasing