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This paper addresses stochastic correlative learning as the basis for a broadly defined class of statistical learning algorithms known collectively as the algorithm of pattern extraction (ALOPEX) family. Starting with the neurobiologically motivated Hebb's rule, the two conventional forms of the ALOPEX algorithm are derived, followed by a modified variant designed to improve the convergence speed. We next describe two more elaborate versions of the ALOPEX algorithm, which incorporate particle filtering that exemplifies a form of Monte Carlo simulation, to exchange computational complexity for an improved convergence and tracking behavior. In support of the different forms of the ALOPEX algorithm developed herein, we present three different experiments using synthetic and real-life data on binocular fusion of stereo images, on-line prediction, and system identification.