Central limit theorems for interacting innovation processes, related statistical tools and general results

TL;DR

This paper analyzes a network of interacting innovation processes modeled as urns with infinitely many colors, deriving central limit theorems and developing statistical tools to infer influence structures, validated on Reddit and Gutenberg datasets.

Contribution

It extends classical urn models to interacting systems, providing new theoretical results and statistical methods for understanding influence dynamics in complex innovation networks.

Findings

Derived second-order asymptotic behavior for interacting urns.

Developed statistical tools for influence inference.

Validated methods on real-world datasets from Reddit and Gutenberg.

Abstract

We study a networked system of innovation processes, where each process is modeled as an urn with infinitely many colors-a classical framework for capturing the emergence of novelties. Extending this paradigm, we analyze a model of interacting urns, where the probability of generating or reusing elements in one process is influenced by the histories of others. This interaction is governed by two matrices that control innovation triggering and reinforcement dynamics across the system. The core contribution of this work is a detailed analysis of the second-order asymptotic behavior of the model. Building on these theoretical results, we develop statistical tools to infer the structure and strength of inter-process influence. The methodology is framed in a general setting, making it broadly applicable. We validate our approach with applications to two real-world datasets from Reddit discussions and Gutenberg text corpora.