Neural Decoding Using Generative BMI Models - Brain-Machine Interface Engineering - page 168

Figure 5.13 shows the predicted hand trajectories of each modeling approach, superimposed
over the desired (actual) arm trajectories for the test data; for simplicity, we only plot the trajectory
along the z coordinate. Qualitatively, we can see that the ICHMM performs better than the others
in terms of reaching targets. Overall, prediction performance of the ICHMM classifier is slightly
better than the VQ-HMM classifier, and superior to the single linear predictor, as evidenced by the
average CCs (across the three coordinates) of 0.64, 0.80, and 0.86 for the single linear predictor, the
bimodel system with VQ-HMM and the bimodel system with ICHMM.
5.6 SUMMaRy
In brain-machine interfaces, the Kalman filter method can provide a rigorous and well-understood
framework to model the encoding of hand movement in motor cortex, and for inferring or decoding
this movement from the firing rates of a cell population. When the restrictive Gaussian assumptions
and linear system model holds, the Kalman filter algorithm provides an elegant analytic optimal
solution to the tracking problem. If one assumes that the observation time-series (neural activity) is
generated by a linear system, then the tuning can be optimally estimated by a linear filter. The sec-
ond assumption of Gaussianity of the posterior density of the kinematic stimulus given the neural
spiking activities reduces all the richness of the interactions to second order information (mean and
the covariance). These two assumptions may be too restrictive for BMI applications and may be
overcome with methods such as particle filtering.
Unfortunately, in the BMI application this particular formulation is also faced with problems
of parameter estimation. The generative model is required to find the mapping from the low-di-
mensional kinematic parameter state space to the high-dimensional output space of neuronal firing
patterns (100+ dimensions). Estimating model parameters from the collapsed space to the high-
dimensional neural can be difficult and yield multiple solutions. For this modeling approach, our
use of physiological knowledge in the framework of the model actually complicates the mapping
process. As an alternative, one could disregard any knowledge about the system and use a strictly
data-driven methodology to build the model. However, if the distributions are not constrained to
be Gaussian, but can be described by unbiased consistent means and covariance, the filter can still
be optimally derived using a least squared argument.
For the HMMs, the results presented here show that the final prediction performance of the
bimodel system using the ICHMM is much better than using the VQ-HMM, and superior to that
of a single linear predictor. Overall, the ICHMM produces good results with few parameters. The
one caveat to the ICHMM is the reliance on the ζ threshold. Fortunately, this threshold is retriev-
able from the training set. Interestingly, the ζ threshold can be viewed as global weighting for the
two classes in this system. If one frames the ICHMM as mixture of experts (ME) perhaps boosting or
bagging could be used to locally weight these simplistic classifiers in future work. The ME generates