Jonathan E. Taylor - US grants

ABSTRACT
PI: Jonathan Taylor
proposal: 0405970

The focus of this proposal is the study hitting probabilities for smooth vector-valued random fields with independent, identically distributed Gaussian processes as components. These models can be used to build a variety of non-Gaussian real-valued processes, though they are closely related to Gaussian processes. The smoothness of the processes allows many tools from point processes to be used in studying these hitting probabilities. These point processes, based on critical points of the process yield an explicit representation for the hitting probability as well as an accurate approximation, the so-called expected Euler characteristic approximation. The proposal seeks to extend recent work of the investigator and collaborators on real-valued Gaussian processes to these non-Gaussian models. Insight gained from these models should prove useful in studying other non-Gaussian models.

The practical motivation for this proposal is in its application to estimating the Family Wise Error Rate (FWER) in neuroimaging activation studies. This FWER is important in determining which areas in a neuroimaging study are associated with a given experimental task. In these studies, psychologists are able to collect space-time recordings of activation in the human brain (more precisely, they can record something associated with activation known as the BOLD signal). They are then able to study which areas are activated by their task, which might be a visual task, an auditory task, etc. Having collected the data, the psychologists are faced with the task of determining which perceived activations are true activations. The results of this proposal help psychologists in this decision, by allowing the psychologists to only accept results with a prespecified FWER. The proposal builds on earlier results in the literature, and extends them to more complicated models of activation.

The investigators in this proposal study two different aspects of noise in neuroimaging data: structure of non-Gaussian random fields and their applications to neuroimaging; along with interpretable predictive modelling of fMRI. The structure of non-Gaussian random fields is expected to shed light on how useful Random Field Theory (RFT), presently used for controlling Family Wise Error Rate (FWER) in neuroimaging studies, can be expected to be for truly non-Gaussian fields. The predictive models proposed by the investigators place much emphasis on interpretability and will allow comparison with the usual approaches based on detecting correlation between experimental stimuli and neuroimaging data while controlling FWER or False Discovery Rate (FDR).

This project is motivated by the need for flexible and valid statistical procedures to interpret neuroimaging data and to confirm neuroscientific hypotheses derived from previous work. Examples of such neuroimaging data can be found in fields like social neuroscience, which seeks to understand and model human social behaviour based on the activation and interactions of various regions of the human brain; neuroeconomics, which seeks to interpret and model some of the decision-making processes of humans based on models of the human brain; and disease models such as schizophrenia in which the goal is to understand how the brains of schizophrenic patients differ in anatomy and function from those of non-schizophrenic patients. Virtually all neuroimaging data is what is known as "high-throughput" which means that huge amounts of data are recorded, typically for only a small group of individuals. Statistical tools are needed to produce consistent and reproducible results from such data. The investigators in this proposal will develop tools that can be used to confirm existing hypotheses about neuroimaging data, as well as generate hypotheses via interpretable predictive models of decision making processes.

Recent developments in molecular neuroscience allow scientists to both optically record neuronal activity and to cause neurons to fire by stimulating them with light. In genetic model organisms like zebrafish and mice, these technologies can be used to observe and manipulate the activity patterns of thousands of neurons at once using non-invasive all-optical methods. While such techniques promise to revolutionize how we look at brain circuits, neural circuits are fundamentally three-dimensional structures. As a result, optical tools able to both image and selectively stimulate 3D volumes of brain tissue must be developed.

This project will develop a device that can record a volume of neurons at each camera exposure, extract information from thousands of these neurons over time, and then use this information to choose which groups of individual neurons in the volume to stimulate with light. This feedback loop will allow scientists to test causal hypotheses about brain network function and its relationship to behavior in a fast and powerful way, leveraging feedback-control technologies currently used in robotics and aeronautics to build and refine dynamical models of the brain online. At the core of this device are new developments in computational microscopy: the light field microscope (LFM), which can computationally reconstruct an entire volume from a single snapshot, and the light field illuminator (LFI), which can create (nearly) arbitrary patterns of light in three dimensions. The project will couple these two devices and accelerate their performance using commercial graphics cards (GPUs) to allow real-time control of biological neural networks in behaving animals.

Project outcomes, including scientific findings resulting from the application of the device to biological specimens, detailed directions on how to construct the physical device, and free, open-source software to run the device, will be provided online at http://graphics.stanford.edu/projects/lfmicroscope/.

This project is focused on structured high dimensional regression with the term structure meant to distinguish the methods from other methods such as l1 minimization methods. Generally speaking, this structure is assumed a priori and is chosen on the basis of finding an interpretable solution to a regression problem. In this project, structure often refers to spatial structure found in areas of application such as neuroimaging or astronomical data. The project has two principal goals. First to develop scalable, flexible algorithms and software implementations for fitting such structured models. Secondly, to understand the statistical performance of such models as well as the algorithms used to fit such models.

The results of the research proposed in this project will allow researcher in the field of neuroscience to improve neuroscientists' ability to predict behavior based on fMRI or other spatio-temporally structured data.