A Genetic Learning Algorithm for the Analysis of Complex Data

A genetic learning algorith m modeled after biological evolution is pres ente d to discern patterns relati ng one observable t hat is taken to be dep endent on many others. T he problem is reduced to an optimization pr oced ure over a space of conditions on th e independent variables. The optimi zation is p erformed by a genetic learning algorithm , using an information t heoret ic fitness fun ction on conditional probability distributions, all derived from dat a that has a very spars e distribution over a very high-dimensional space. Vole will discuss applications in forec asting, management , weat her, neu roan alysis, larg e-scale modeling , and ot her areas. Introduct ion We cons ider d a t a obtaine d from a complex sys te m, i.e ., a system wit h m an y d egrees of fr eedom that are highly coupled. Su ch dat a a re usu ally b eset wi th two problems : (i) randomness , from ob servational errors , from low-dimen sional chaotic dynamics , an d from hi gh-di m en sional n oise, and (ii) limitations on t he am ou nt of d ata ava ilable. We wi ll presen t a metho d for finding p atterns in t h is data , especially app licable wh en no simp le p at t erns are r eadily d iscernible. We will assume the d at a to b e a collection of p airs where each x = (Xl ,'. . , x n) is interp ret ed as a set of indep endent var ia bles on which t he corresp on ding y is presumed t o b e dependen t. Obser vation s of each (x ,V) p air are ob t ained fro m a m ea surement t hat in evitably h as a fini t e resolution , so va lues of t hese va r ia bl es will take on one of a di scr ete set