Learning Stochastic Perceptrons Under k-Blocking Distributions
Mario Marchand, Saeed Hadjifaradji · 1994
We present a statistical method that PAC learns the class of stochastic perceptrons with arbitrary monotonic activation function and weights w i #{-1,0,+1} when the probability distribution that generates the input examples is member of a family that we call k-blocking distributions. Such distributions represent an important step beyond the case where each input variable is statistically independent since the 2k-blocking family contains all the Markov distributions of order k. By stochastic perceptron we mean a perceptron which, upon presentation of input vector x, outputs 1 with probability f( P i w i x i - #). Because the same algorithm works for any monotonic (nondecreasing or nonincreasing) activation function f on Boolean domain, it handles the well studied cases of sigmods and the "usual" radial basis functions. 1 INTRODUCTION Within recent years, the field of computational learning theory has emerged to provide a rigorous framework for the design and analysi...