  Stochastic neural networks are a prototypical computational device able to
build a probabilistic representation of an ensemble of external stimuli.
Building on the relationship between inference and learning, we derive a
synaptic plasticity rule that relies only on delayed activity correlations, and
that shows a number of remarkable features. Our "delayed-correlations matching"
(DCM) rule satisfies some basic requirements for biological feasibility: finite
and noisy afferent signals, Dale's principle and asymmetry of synaptic
connections, locality of the weight update computations. Nevertheless, the DCM
rule is capable of storing a large, extensive number of patterns as attractors
in a stochastic recurrent neural network, under general scenarios without
requiring any modification: it can deal with correlated patterns, a broad range
of architectures (with or without hidden neuronal states), one-shot learning
with the palimpsest property, all the while avoiding the proliferation of
spurious attractors. When hidden units are present, our learning rule can be
employed to construct Boltzmann machine-like generative models, exploiting the
addition of hidden neurons in feature extraction and classification tasks.
