  Identification of patterns from discrete data time-series for statistical
inference, threat detection, social opinion dynamics, brain activity prediction
has received recent momentum. In addition to the huge data size, the associated
challenges are, for example, (i) missing data to construct a closed
time-varying complex network, and (ii) contribution of unknown sources which
are not probed. Towards this end, the current work focuses on statistical
neuron system model with multi-covariates and unknown inputs. Previous research
of neuron activity analysis is mainly limited with effects from the spiking
history of target neuron and the interaction with other neurons in the system
while ignoring the influence of unknown stimuli. We propose to use unknown
unknowns, which describes the effect of unknown stimuli, undetected neuron
activities and all other hidden sources of error. The maximum likelihood
estimation with the fixed-point iteration method is implemented. The
fixed-point iterations converge fast, and the proposed methods can be
efficiently parallelized and offer computational advantage especially when the
input spiking trains are over long time-horizon. The developed framework
provides an intuition into the meaning of having extra degrees-of-freedom in
the data to support the need for unknowns. The proposed algorithm is applied to
simulated spike trains and on real-world experimental data of mouse
somatosensory, mouse retina and cat retina. The model shows a successful
increasing of system likelihood with respect to the conditional intensity
function, and it also reveals the convergence with iterations. Results suggest
that the neural connection model with unknown unknowns can efficiently estimate
the statistical properties of the process by increasing the network likelihood.
