MIC theory proof with its application
Dongsheng Wang · Advances in computer science research · 2024
Measuring dependencies between two variables in an extremely large data set is an increasingly important problem, naturally then the methods to solve such problems warrants equal if not greater attention.This paper aims to overview an effective measure of dependence, the MIC.This statistical measure is equitable giving no preference to certain function types.It is also general, being able to analyze both linear and nonlinear function types as well as combinations and superpositions of both.The key methodology such as the definitions and steps of MIC are explained as well as a proof of the central recursive algorithm which allows realistic runtimes for MIC.Other heuristic and approximations that make it both an accurate and efficient algorithm are also covered, namely the purpose and effect of equipartition and the clumping of the master partition.MICe, an approximation of MIC is also explained.This approximation fully utilizes the two heuristics of equipartition and clumping.This paper also briefly explains why these simplifications can still provide accurate results with a significantly faster runtime.