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Zhao, Mengyuan (2010) STATISTICAL METHODS FOR EXPLORING NEURONAL INTERACTIONS. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Generalized linear models (GLMs) offer a platform for analyzing multi-electroderecordings of neuronal spiking. We suggest an L1-regularized logistic regressionmodel to detect short-term interactions under certain experimental setups. Weestimate parameters of this model using a coordinate descent algorithm; we determinethe optimal tuning parameter using BIC, and prove its asymptotic validity. Simulationstudies of the method's performance show that this model can detect excitatoryinteractions with high sensitivity and specificity with reasonably large recordings,even when the magnitude of the interactions is small; similar results hold forinhibition for sufficiently high baseline firing rates. The method is somewhat robustto network complexity and partial observation of networks. We apply our method tomulti-electrode recording data from monkey dorsal premotor cortex (PMd). Our resultspoint to certain features of short-term interactions when a monkey plans a reach.Next, we propose a variable coefficients GLM model to assess the temporal variationof interactions across trials. We treat the parameters of interest as functions overtrials, and fit them by penalized splines. There are also nuisance parameters assumedconstant, which are mildly penalized to guarantee the finite maximum of thelog-likelihood. We choose tuning parameters for smoothness by generalized crossvalidation, and provide simultaneous confidence bands and hypothesis tests fornull models. To achieve efficient computation, some modifications are also made. Weapply our method to a subset of the monkey PMd data. Before the implementation to thereal data, simulations are done to assess the performance of the proposed model.Finally, for the logistic and Poisson models, one possible difficulty is that iterativealgorithms for estimation may not converge because of certain data configurations(called complete and quasicomplete separation for the logistic). We show that thesefeatures are likely to occur because of refractory periods of neurons, and show howstandard software deals with this difficulty. For the Poisson model, we show that suchdifficulties arise possibly due to bursting or specifics of the binning. Wecharacterize the nonconvergent configurations for both models, show that they can bedetected by linear programming methods, and propose remedies.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Zhao, Mengyuanmez25@pitt.eduMEZ25
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairIyengar, Satishssi@pitt.eduSSI
Committee MemberBatista, Aaron Papb10@pitt.eduAPB10
Committee MemberGleser, Leon Jgleser@pitt.eduGLESER
Committee MemberKrafty, Robertkrafty@pitt.eduKRAFTY
Date: 1 October 2010
Date Type: Completion
Defense Date: 25 June 2010
Approval Date: 1 October 2010
Submission Date: 22 July 2010
Access Restriction: 5 year -- Restrict access to University of Pittsburgh for a period of 5 years.
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: across-trial variation; BIC; Bayesian confidence bands; GCV; infinite MLEs; L1 regularization; logistic regression; penalized splines; quasi complete separation; vary coefficients models; coordinate descent; Generalized linear models; likelihood ratio test; complete separation
Other ID:, etd-07222010-142247
Date Deposited: 10 Nov 2011 19:52
Last Modified: 15 Nov 2016 13:46


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