Latent variable models for neural data analysis
The brain is perhaps the most complex system to have ever been subjected to rigorous scientific 
investigation. The scale is staggering: over 10^11 neurons, each making an average of 10^3 synapses, 
with computation occurring on scales ranging from a single dendritic spine, to an entire cortical 
area. Slowly, we are beginning to acquire experimental tools that can gather the massive amounts 
of data needed to characterize this system. However, to understand and interpret these data will 
also require substantial strides in inferential and statistical techniques. This dissertation attempts 
to meet this need, extending and applying the modern tools of latent variable modeling to problems 
in neural data analysis. It is divided into two parts. The first begins with an exposition of the general techniques of 
latent variable modeling. A new, extremely general, optimization algorithm is proposed - called 
Relaxation Expectation Maximization (REM) - that may be used to learn the optimal parameter 
values of arbitrary latent variable models. This algorithm appears to alleviate the common problem 
of convergence to local, sub-optimal, likelihood maxima. REM leads to a natural framework for 
model size selection; in combination with standard model selection techniques the quality of fits may 
be further improved, while the appropriate model size is automatically and efficiently determined. 
Next, a new latent variable model, the mixture of sparse hidden Markov models, is introduced, and 
approximate inference and learning algorithms are derived for it. This model is applied in the second 
part of the thesis. The second part brings the technology of part I to bear on two important problems in experimental 
neuroscience. The first is known as spike sorting; this is the problem of separating the spikes 
from different neurons embedded within an extracellular recording. The dissertation offers the first 
thorough statistical analysis of this problem, which then yields the first powerful probabilistic solution. 
The second problem addressed is that of characterizing the distribution of spike trains recorded 
from the same neuron under identical experimental conditions. A latent variable model is proposed. 
Inference and learning in this model leads to new principled algorithms for smoothing and clustering 
of spike data.