What are the computations of the cerebellum, the basal ganglia and the cerebral cortex?

The classical notion that the cerebellum and the basal ganglia are dedicated to motor control is under dispute given increasing evidence of their involvement in non-motor functions. Is it then impossible to characterize the functions of the cerebellum, the basal ganglia and the cerebral cortex in a simplistic manner? This paper presents a novel view that their computational roles can be characterized not by asking what are the "goals" of their computation, such as motor or sensory, but by asking what are the "methods" of their computation, specifically, their learning algorithms. There is currently enough anatomical, physiological, and theoretical evidence to support the hypotheses that the cerebellum is a specialized organism for supervised learning, the basal ganglia are for reinforcement learning, and the cerebral cortex is for unsupervised learning.This paper investigates how the learning modules specialized for these three kinds of learning can be assembled into goal-oriented behaving systems. In general, supervised learning modules in the cerebellum can be utilized as "internal models" of the environment. Reinforcement learning modules in the basal ganglia enable action selection by an "evaluation" of environmental states. Unsupervised learning modules in the cerebral cortex can provide statistically efficient representation of the states of the environment and the behaving system. Two basic action selection architectures are shown, namely, reactive action selection and predictive action selection. They can be implemented within the anatomical constraint of the network linking these structures. Furthermore, the use of the cerebellar supervised learning modules for state estimation, behavioral simulation, and encapsulation of learned skill is considered. Finally, the usefulness of such theoretical frameworks in interpreting brain imaging data is demonstrated in the paradigm of procedural learning.