STDP (spike timing dependent plasticity) is a learning rule for changing the synaptic weights between neurons. It is Hebbian-like in that the weight changes depend on the coincidence of pre- and post-synaptic spikes, but it includes a notion of causation in that the synapse is strengthened if a presynaptic spike precedes a postsynaptic spike, but the synapse is weakened if a postsynaptic spike precedes a presynaptic spike.
Rate neurons are often used in simulations because they are computationally cheap compared to simulating spiking neurons. In order to implement STDP, spikes are generated using an inhomogeneous Poisson process with the rate parameter defined by the current rate of the rate neuron.
What I would like to know is whether a shortcut has been developed to calculate the weight changes due to STDP directly from the temporal dynamics of the pre- and post-synaptic weights without having to explicitly generate spike times through a poisson process.
Any help?
The appropriate way to do this is to find the cross-correlation of the time series of rates of the two neurons. Then take the dot product of the cross correlation with the STDP kernel (i.e., the integral of the correspondence at each point in the STDP window between how much STDP "likes" cross correlation at that lag and how much cross correlation there actually was at that lag). This gives a value that, when properly scaled, tells you the amount of weight change that synapse should receive.
Have you looked at the Izhikevich model, which uses a spiking network of 1000 cortical neurons with dopamine-modulated STDP to adjust synaptic weights? (Cerebral Cortex doi:10.1093/cercor/bhl152). Apologies of you are already aware of this and it does not help with your question (I'm not a modeller) but it certainly makes good inferences for the need for causality of pre and post synaptic activity in a sea of slower timescale reward events.
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