Mean-Field Theory of Meta-learning

Abstract

A Ab bs st tr ra ac ct tWe discuss here the mean-field theory for a cellular automata model of meta-learning. The metalearning is the process of combining outcomes of individual learning procedures in order to determine the final decision with higher accuracy than any single learning method. Our method is constructed from an ensemble of interacting, learning agents, that acquire and process incoming information using various types, or different versions of machine learning algorithms. The abstract learning space, where all agents are located, is constructed here using a fully connected model that couples all agents with random strength values. The cellular automata network simulates the higher level integration of information acquired from the independent learning trials. The final classification of incoming input data is therefore defined as the stationary state of the meta-learning system using simple majority rule, yet the minority clusters that share opposite classification outcome can be observed in the system. Therefore, the probability of selecting proper class for a given input data, can be estimated even without the prior knowledge of its affiliation. The fuzzy logic can be easily introduced into the system, even if learning agents are build from simple binary classification machine learning algorithms by calculating the percentage of agreeing agents.

Modeling of Cognitive Agents

“…First, the social strengths of all members of the whole group; secondly, their social distance from the selected individual; and finally their total number N. Kohring [16,17] extended Latane's theory to include learning. Plewczynski [18,19] solved analytically the model in the continuous limit and the Cartesian space with learning rules. Hołyst et al performed numerical simulations in simplified geometries, also provided the mean-field approximation of the social impact theory [20][21][22][23].…”