Starting from the problem of density estimation, it is shown that Expectation Maximization (EM) learning can be considered a Hebbian mechanism. From this, it is possible to outline a theory of self-organization of cortical maps, which is based on a well-defined optimization process and preserves biologically desirable characteristics such as local computation and uniform treatment of input and lateral connections. A thalamocortical network is described that implements the theory in a fully distributed manner: it uses cortical dynamics for the E-step and Hebbian adaptation of cortico-cortical connections at steady state for the M-step.