Biomedical Engineering Reference
In-Depth Information
onto the linear filter direction. The kernel-smoothed histogram of spike-triggered velocity vectors
filtered by
k
is an approximation of the joint PDF
p s
( pike,
k v
projected to the linear filter direc-
×
)
tion. The ratio actually obeys the Bayesian formulation:
p
(spike,
k v
×
)
p
(spike |
k v
× =
)
(6.18)
p k v
(
×
)
Figure
6.8
depicts the marginal PDF
×
p k v
, which is the blue line in the top plot, and the joint
(
)
PDF
p k v
, which is represented by the red line in the top plot, computed for neuron 110.
The nonlinear estimation for
f
is shown in the bottom plot of Figure
6.8
. The
x
axis is the
range of the filtered multidimensional velocity vectors. The
y
axis is the corresponding instanta-
neous conditional probability of spike given the linear filter output. The accuracy of the nonlinear
function estimation is not constant across the range, and this may explain the ripples seen at the
extremes of the range, so regularization should be utilized. This
f
is estimated from the real data,
(spike,
×
)
FIgURE 6.:
Nonlinear tuning estimation for neuron 110.
