  Learning and memory in the brain are implemented by complex, time-varying
changes in neural circuitry. The computational rules according to which
synaptic weights change over time are the subject of much research, and are not
precisely understood. Until recently, limitations in experimental methods have
made it challenging to test hypotheses about synaptic plasticity on a large
scale. However, as such data become available and these barriers are lifted, it
becomes necessary to develop analysis techniques to validate plasticity models.
Here, we present a highly extensible framework for modeling arbitrary synaptic
plasticity rules on spike train data in populations of interconnected neurons.
We treat synaptic weights as a (potentially nonlinear) dynamical system
embedded in a fully-Bayesian generalized linear model (GLM). In addition, we
provide an algorithm for inferring synaptic weight trajectories alongside the
parameters of the GLM and of the learning rules. Using this method, we perform
model comparison of two proposed variants of the well-known
spike-timing-dependent plasticity (STDP) rule, where nonlinear effects play a
substantial role. On synthetic data generated from the biophysical simulator
NEURON, we show that we can recover the weight trajectories, the pattern of
connectivity, and the underlying learning rules.
