Estimation of Graphical Models for a class of Multivariate Skew-Symmetric Distributions
Date: 26 June 2020, Friday
Time: 4pm
Speaker: Dr Linh Nghiem (ANU)
Abstract:
We consider the problem of estimating graphical models for data generated from a class of multivariate skew symmetric distributions, which can be used to model multivariate data with both moderate skewness and heavy tails. Conditional independence between any component requires both the corresponding element of the inverse covariance matrix and the product of the two corresponding components in the shape vector to be zero. Utilizing new properties of the conditional expectation in this class of distributions, we propose a novel two-step nodewise approach to estimate the graphical model. For each nodewise regression, we first fit a linear model using least squares, and then fit a one-component projection pursuit regression on the residual obtained from the first step. The graph is estimated by thresholding an appropriate quantity from all the nodewise regressions. We prove consistency of the estimated graph in a setting that allows both the sample size and the number of variables to diverge. Simulation results show the superior performance of the new method in estimating the true graphical model compared to common methods that are used for estimating the Gaussian graphical model. Finally, the new method is applied on a dataset regarding the physicochemical properties of wine.
Link: https://au.bbcollab.com/guest/fcf219c74ac743e89565a9e6e8d349a9
Video:
Date: 26 June 2020, Friday
Time: 4pm
Speaker: Dr Linh Nghiem (ANU)
Abstract:
We consider the problem of estimating graphical models for data generated from a class of multivariate skew symmetric distributions, which can be used to model multivariate data with both moderate skewness and heavy tails. Conditional independence between any component requires both the corresponding element of the inverse covariance matrix and the product of the two corresponding components in the shape vector to be zero. Utilizing new properties of the conditional expectation in this class of distributions, we propose a novel two-step nodewise approach to estimate the graphical model. For each nodewise regression, we first fit a linear model using least squares, and then fit a one-component projection pursuit regression on the residual obtained from the first step. The graph is estimated by thresholding an appropriate quantity from all the nodewise regressions. We prove consistency of the estimated graph in a setting that allows both the sample size and the number of variables to diverge. Simulation results show the superior performance of the new method in estimating the true graphical model compared to common methods that are used for estimating the Gaussian graphical model. Finally, the new method is applied on a dataset regarding the physicochemical properties of wine.
Link: https://au.bbcollab.com/guest/fcf219c74ac743e89565a9e6e8d349a9
Video: