Zhang, Yao
(2010)
Statistical Treatment of Gravitational Clustering Algorithm.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
In neuroscience, simultaneously recorded spike trains from multiple neurons are increasingly common; however, the computational neuroscience problem of how to quantitatively analyze such data remains a challenge. Gerstein, et al. proposed a gravitational clustering algorithm (GCA) for multiple spike trains to qualitatively study interactions, in particular excitation, among multiple neurons. This thesis is mainly focused on a probabilistic treatment of GCA and a statistical treatment of Gerstein's interaction mode.For a formal probabilistic treatment, we adopt homogeneous Poisson processes to generate the spike trains; define an interaction mode based on Gerstein's formulation; analyze the asymptotic properties of its cluster index -- GCA distances (GCAD). Under this framework, we show how the expectation of GCAD is related to a particular interaction mode, i.e., we prove that a time-adjusted-GCAD is a reasonable cluster index for large samples. We also indicate possible stronger results, such as central limit theorems and convergence to a Gaussian process. In our statistical work, we construct a generalized mixture model to estimate Gerstein's interaction mode. We notice two key features of Gerstein's proposal: (1) each spike from each spike train was assumed to be triggered by either one previous spike from one other spike train or environment; (2) each spike train was transformed into a continuous longitudinal curve. Inspired by their work, we develop a Bayesian model to quantitatively estimate excitation effects in the network structure. Our approach generalizes the mixture model to accommodate the network structure through a matrix Dirichlet distribution. The network structure in our model could either approximate the directed acyclic graph of a Bayesian network or be the directed graph in a dynamic Bayesian network. This model can be generally applied on high-dimensional longitudinal data to model its dynamics. Finally, we assess the sampling properties of this model and its application to multiple spike trains by simulation.
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| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
1 October 2010 |
| Date Type: |
Completion |
| Defense Date: |
19 December 2009 |
| Approval Date: |
1 October 2010 |
| Submission Date: |
22 April 2010 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Statistics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Bayes network; generalized mixture model; high-dimensional longitudinal data; matrix Dirichlet distribution; multiple spike trains; Poisson process |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-04222010-053115/, etd-04222010-053115 |
| Date Deposited: |
10 Nov 2011 19:41 |
| Last Modified: |
15 Nov 2016 13:41 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/7513 |
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