Neuroscience is entering the age of big data, due to technological advances in

electrical and optical recording techniques. Where historically neuroscientists have

only been able to record activity from single neurons at a time, recent advances

allow the measurement of activity from multiple neurons simultaneously. In fact, this

advancement follows a Moore’s Law-style trend, where the number of simultaneously

recorded neurons more than doubles every seven years, and it is now common to see

simultaneous recordings from hundreds and even thousands of neurons.

The consequences of this data revolution for our understanding of brain struc-

ture and function cannot be understated. Not only is there opportunity to address

old questions in new ways, but more importantly these experimental techniques will

allow neuroscientists to address new questions entirely. However, addressing these

questions successfully requires the development of a wide range of new data anal-

ysis tools. Many of these tools will draw on recent advances in machine learning

and statistics, and in particular there has been a push to develop methods that can

accurately model the statistical structure of high-dimensional neural activity.

In this dissertation I develop a latent variable modeling framework for analyz-

ing such high-dimensional neural data. First, I demonstrate how this framework can

be used in an unsupervised fashion as an exploratory tool for large datasets. Next, I

extend this framework to incorporate nonlinearities in two distinct ways, and show

that the resulting models far outperform standard linear models at capturing the

structure of neural activity. Finally, I use this framework to develop a new algorithm

for decoding neural activity, and use this as a tool to address questions about how

information is represented in populations of neurons.