Statistical inference for interacting innovation processes and related general results

2025-01-16

AI Summary

This paper studies networked innovation processes, where each process is modeled as an infinite-color Pólya urn to capture novelty emergence. Addressing the limitation of existing models—which ignore historical interdependencies among processes—we develop, for the first time, a second-order asymptotic theory for interactive innovation processes, characterizing their joint growth rates and covariance structure. We propose a general statistical framework based on intensity function estimation and point-process inference to quantify the direction and magnitude of cross-process influence. The methodology is empirically validated on Reddit community evolution and Gutenberg textual innovation data, demonstrating both theoretical consistency and statistical robustness. Our approach provides a scalable theoretical toolkit and practical methodology for modeling innovation diffusion and conducting causal inference across diverse domains.

Technology Category

Reasoning under Uncertainty: Relational Probabilistic ModelsCognitive Modeling & Cognitive Systems: Computational CreativityKnowledge Representation and Reasoning: Action, Change, and Causality

Application Category

Web Mining and Content Analysis: Models for Web evolutionSocial Networks and Social Media: Computational social scienceGraph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Given the importance of understanding how different innovation processes affect each other, we have introduced a model for a finite system of interacting innovation processes. The present work focuses on the second-order asymptotic properties of the model and illustrates how to leverage the theoretical results in order to make statistical inference on the intensity of the interaction. This methodology is presented within a general framework in the supplementary material to ensure its broad applicability across various contexts. We apply the proposed tools to two real data sets (from Reddit and Gutenberg).

Problem

• Analyzing networked innovation processes with interacting urns
• Studying cross-process influence on novelty emergence dynamics
• Developing statistical tools to infer inter-process influence structure

Innovation

• Interacting urns model with cross-process influence
• Statistical tools infer network influence structure
• Validated on Reddit and Gutenberg datasets