State Space Realization Theorems For Data Mining

TL;DR

This paper develops realization theorems for formal series related to events and profiles in data mining, utilizing Hopf algebra tools to formalize the mathematical foundation of predictive models.

Contribution

It introduces a novel application of Hopf algebra techniques to establish realization theorems for formal series in data mining contexts.

Findings

Proves realization theorems for formal series in data mining.

Uses Hopf algebra framework to analyze event-based models.

Provides mathematical foundation for predictive formal series.

Abstract

In this paper, we consider formal series associated with events, profiles derived from events, and statistical models that make predictions about events. We prove theorems about realizations for these formal series using the language and tools of Hopf algebras.