Biomedical Engineering Reference
In-Depth Information
number is smaller than the probability, then a spike is generated in this time interval. The tuning
function can be shown equivalent to
l
= ×
f k v
with spike
t
= Poisson (
λ
f
).
Figure
6.7
shows one realization of a generated spike train using the estimated tuning func-
tion for neuron 72. The upper plot depicts spikes scaled by ½ because of the temporal resolution
presented in the figure. The blue line is the estimated instantaneous conditional firing probability
×
(
)
t
t
p s k v
, which corresponds to the mean
l
of the inhomogeneous Poisson process. Dur-
ing most of the duration depicted in the figure, the estimated
l
can follow the real spike density
change accurately. The bottom plot displays one realization of spikes generated from the estimated
l
. The total number of spikes 113 is close to the real number of spike 126 during the time length
and the correlation coefficient is between the spike trains smoothed by a Gaussian kernel are shown
in Table
6.2
for different number of realizations. Note that the realizations by the Poisson spike
generator can be quite different.
( pike |
)
6.4.2 Estimating the Nonlinearity in the lNP Model
The nonlinear encoding function
f
for each neuron was estimated using an intuitive nonparametric
binning technique. Given the linear filter vector
k
, we drew the histogram of all the velocity vectors
k
and smoothed the histogram by convolving with a Gaussian kernel. The same procedure
was repeated to draw the smoothed histogram for the outputs of the spike-triggered velocity vectors
filtered by
filtered by
k
. The nonlinear function
f
, which gives the conditional instantaneous firing rate to the
Poisson spike-generating model, was then estimated as the ratio of the two smoothed histograms.
Statistically speaking, the kernel smoothed histogram of all the velocity vectors filtered by
k
is an approximation to the marginal PDF
×
p k v
of the multidimensional velocity vectors projected
(
)
TaBlE 6.2:
Performance as a function of the number of realizations
No. oF REalIZaTIoNS
CoRRElaTIoN CoEFFICIENT
100
0.89
200
0.94
300
0.96
1000
0.98
10 000
0.99
