A general solution to the preferential selection model

TL;DR

This paper presents a comprehensive analytical solution to Herbert Simon's 1955 model for evolving novelty, linking it to network growth models and enabling accurate generative modeling of systems based on occurrence data.

Contribution

It offers the first general analytic solution to Simon's model, connecting it to preferential attachment and providing a high-accuracy generative framework for occurrence-based systems.

Findings

The model accurately reproduces occurrence frequency distributions.

It unifies Simon's model with Barabási's preferential attachment.

Provides a generative approach for systems modeled as types.

Abstract

We provide a general analytic solution to Herbert Simon's 1955 model for time-evolving novelty functions. This has far-reaching consequences: Simon's is a pre-cursor model for Barabasi's 1999 preferential attachment model for growing social networks, and our general abstraction of it more considers attachment to be a form of link selection. We show that any system which can be modeled as instances of types---i.e., occurrence data (frequencies)---can be generatively modeled (and simulated) from a distributional perspective with an exceptionally high-degree of accuracy.