A dynamic Boltzmann machine (DyBM) has been proposed as a model of a spiking
neural network, and its learning rule of maximizing the log-likelihood of given
time-series has been shown to exhibit key properties of spike-timing dependent
plasticity (STDP), which had been postulated and experimentally confirmed in
the field of neuroscience as a learning rule that refines the Hebbian rule.
Here, we relax some of the constraints in the DyBM in a way that it becomes
more suitable for computation and learning. We show that learning the DyBM can
be considered as logistic regression for binary-valued time-series. We also
show how the DyBM can learn real-valued data in the form of a Gaussian DyBM and
discuss its relation to the vector autoregressive (VAR) model. The Gaussian
DyBM extends the VAR by using additional explanatory variables, which
correspond to the eligibility traces of the DyBM and capture long term
dependency of the time-series. Numerical experiments show that the Gaussian
DyBM significantly improves the predictive accuracy over VAR.