Statistical methods addressing certainty and uncertainty in neural representation
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Abstract
Recent advances in neural recording techniques allow experimentalists to record neural activity with higher temporal and spatial resolutions, from a large number of areas of the brain, while a subject performs complex tasks. Furthermore, neuroscience experiments themselves have evolved substantially, and have become more naturalistic and less-controlled. As a result, neural datasets are often much larger and complicated than before and can have properties that make their analysis challenging. This has affected our perspective about different brain mechanisms. For example, researchers view of population coding has changed from the idea that single neurons or small neuronal ensembles code separately and independently for different contexts according to fixed firing patterns, to the idea that large populations of neurons code for different environmental contexts collectively and intermittently, where each neuron may have multiple representations for a fixed context and may exhibit rapid fluctuations between these representations. In order to allow the full potential that these novel experiments offer to be fulfilled, it is crucial to develop and select appropriate analytical tools to analyze data collected from these experiments.
In the first project of my dissertation, I worked on the problem of perfect prediction in Generalized Linear Models (GLMs), which arises when the log-likelihood is maximized in the limit as parameters go to ±∞ and estimators do not have approximate normal distributions. This can happen in many neural systems due to either structural properties such as refractoriness, or incomplete sampling of the signals influencing spiking. This phenomenon not only affects the fitting process of GLMs, but also presents challenges to inference and generalization of resulting models. However, when these issues arise in statistical neural models, researchers often adopt one of a set of ad-hoc methods to avoid dealing with them, and the issues remain unaddressed in their analyses. In this project, we explored a range of different approaches for dealing with these issues in point process GLMs, illustrated their application to fitting a model that leads to perfect prediction, and compare them in terms of their advantages and disadvantages.
In the second and third projects of my dissertation, I developed analytical tools to address the finding that neuronal populations do not always respond uniquely and consistently to fixed stimuli. This can be due to uncontrolled or even unmeasurable factors in the experiment, such as attentional state or the mood of the animal. This phenomenon has been observed more recently, as neuroscience experiments have become more naturalistic, with potentially many uncontrolled variables that can affect neural coding. We developed a novel state-space modeling framework that takes into account the coexistence of multiple representations for a fixed stimulus or context, and use that for remapping analysis in the CA1 region of the hippocampus. We demonstrated that our statistical framework provides useful estimation and inference tools for decoding the perceived environment and measuring uncertainty moment-by-moment, detecting cell populations that code for an environment collectively and intermittently, and investigating the dynamic properties of these populations.
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