Topologically ordered competitive sampling

-An tmportant problem in nonparametrtc modehng ts the selecHon of samples from an mdependent and Mentwally dtstrtbuted observatton (liD) process such that the resultmg sample ensemble forms a prototyptcal model of the observaHon process. Thts paper discusses a sampling techmque that is closely related to topologtcally ordered compettttve learning In the context of a ttghtly constrained notton of topologtcal ordering, the proposed samphng algortthm uses a randomized winner-take-all rule to modify sample ensembles m a way that generates a reverstble Markov chain The stattonary denstty for thts reversible chain ts exphcttly computed and used to charactertze the samphng procedure's steady-state staustwal behavtour Thts charactertzatwn shows that topologwally ordered compettttve samphng can generate steady-state sample ensembles that form equt-probable partttlons of the observation space More tmportantly, thts paper provMes a formal analyttcal framework that can be used as a model for the analysts of other competttwe learnmg paradtgms Keywords--Competitve learning, Nonparametnc density estimation, Topological ordering.