Presented By: Department of Statistics
Network Inference with Applications in Neuroimaging
Qianhua Shan
Abstract:
With network data becoming ubiquitous in many applications, many models and algorithms for network analysis have been proposed. Besides the commonly studied single binary network, in which each node in the network represents a single object and the edge between two nodes represents the relationship between the two, multiple weighted networks are also frequently observed in neuroimaging. In such applications, a network can be observed for each individual, with all networks sharing the same set of nodes. In this thesis, we develop inference methods for both types of network with application to neuroimaging dataset.
For a single binary network, there exists many inference models. Yet methods for providing uncertainty estimates in addition to point estimates of network parameters are much less common. Bootstrap and other resampling procedures have been an effective general tool for estimating uncertainty from i.i.d. samples, resampling network data is substantially more complicated. In Chapter 1, we compare three different network resampling procedures from the point of view of uncertainty estimation, and propose a general procedure to construct confidence intervals for network parameters through network resampling. We find that no one procedure is universally best for all tasks, and demonstrate the pros and cons of different resampling strategies through simulation studies.
In Chapter 2, based on the motivating example of Adolescent Brain Cognitive Development (ABCD) study, we proposed an algorithm for fitting multiple response regression problems where predictors are weighted network and edge weights are used as features. While most multiple response regression methods take advantage of correlated responses by incorporating covariance structure in the error vector, the method we proposed also considers the additional information provided in network-valued predictors by adding the constraint that a common community structure is shared across different prediction coefficients. We apply the method to the ABCD dataset, and provide inference on the relationship between rest-state brain fMRI networks and multiple cognitive task performance of 9-10 year old adolescence.
While learning the community structure shared across regression coefficients corresponding to different cognitive tasks allows better interpretation of the partition of brain areas, a discrete community assignment might impose a constraint that is too strong to remain the predictive power of brain connectomes. In Chapter 3, we relax the constraint to shared low rank structure across regression coefficients, and compared the performance of common structures learnt through three different methods, namely the low rank structure and the mixed membership structure in the coefficient of common cognitive ability, and the shared low rank embeddings in all task-specific regression coefficients.
With network data becoming ubiquitous in many applications, many models and algorithms for network analysis have been proposed. Besides the commonly studied single binary network, in which each node in the network represents a single object and the edge between two nodes represents the relationship between the two, multiple weighted networks are also frequently observed in neuroimaging. In such applications, a network can be observed for each individual, with all networks sharing the same set of nodes. In this thesis, we develop inference methods for both types of network with application to neuroimaging dataset.
For a single binary network, there exists many inference models. Yet methods for providing uncertainty estimates in addition to point estimates of network parameters are much less common. Bootstrap and other resampling procedures have been an effective general tool for estimating uncertainty from i.i.d. samples, resampling network data is substantially more complicated. In Chapter 1, we compare three different network resampling procedures from the point of view of uncertainty estimation, and propose a general procedure to construct confidence intervals for network parameters through network resampling. We find that no one procedure is universally best for all tasks, and demonstrate the pros and cons of different resampling strategies through simulation studies.
In Chapter 2, based on the motivating example of Adolescent Brain Cognitive Development (ABCD) study, we proposed an algorithm for fitting multiple response regression problems where predictors are weighted network and edge weights are used as features. While most multiple response regression methods take advantage of correlated responses by incorporating covariance structure in the error vector, the method we proposed also considers the additional information provided in network-valued predictors by adding the constraint that a common community structure is shared across different prediction coefficients. We apply the method to the ABCD dataset, and provide inference on the relationship between rest-state brain fMRI networks and multiple cognitive task performance of 9-10 year old adolescence.
While learning the community structure shared across regression coefficients corresponding to different cognitive tasks allows better interpretation of the partition of brain areas, a discrete community assignment might impose a constraint that is too strong to remain the predictive power of brain connectomes. In Chapter 3, we relax the constraint to shared low rank structure across regression coefficients, and compared the performance of common structures learnt through three different methods, namely the low rank structure and the mixed membership structure in the coefficient of common cognitive ability, and the shared low rank embeddings in all task-specific regression coefficients.
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