Statistical Analysis on Tree-Structured Objects

Sienkiewicz, E. and Wang, H. (2017). Pareto Quantiles of Unlabeled Tree Objects. Accepted by the Annals of Statistics.

Chang, H.-W., Iyer, H., Bullitt, E. and Wang, H. (2013). Generalized Linear Mixed Models for Branching Probabilities of Brain Artery Systems. Model Assisted Statistics and Applications, 8, 121-133.

Wang, Y., Marron, J.S., Aydin, Ladha, A., Bullitt, E. and Wang, H. (2012). A Nonparametric Regression Model with Tree-structured Response. Journal of the American Statistical Association, 107, 1272-1285.

Aydin, B., Pataki, G., Wang, H., Ladha, A., Bullitt, E. and Marron, J.S. (2012). New Approaches to Principal Component Analysis. Accepted by Statistics in Biosciences, 4, 132-156.

Aydin, B., Pataki, G., Wang, H., Ladha, A., Bullitt, E. and Marron, J.S. (2011). Visualizing the Structure of Large Trees. Electronic Journal of Statistics, 5, 405-420.

Aydin, B., Pataki, G., Wang, H. , Bullitt, E. and Marron, J.S. (2009). A Principal Component Analysis for Trees. The Annals of Applied Statistics, 3, 1597-1615.

Wang, H. and Marron, J. S. (2007). Object Oriented Data Analysis: Sets of Trees. The Annals of Statistics, 35, 1849-1873

 

Supplemental Material

Generalized Linear Mixed Models for Branching Probabilities of Brain Artery Systems.

A draft of the paper can be downloaded Here.

A Nonparametric Regression Model with Tree-structured Response.

A draft of the paper can be downloaded Here. The supplemental material can be downloaded Here.

Here are some supplemental movies for the simulation study in this paper:

Visualizing the Structure of Large Trees.

A draft of the paper can be downloaded Here or arXiv.

A Principal Component Analysis for Trees.

A draft of the paper: arXiv

Here are some supplemental figures for this paper:

  • The support trees of 3 sub-populations for two correspondences: ST
  • For descendant correspondence, the first three principal components for three sub-populations: Lines
  • For left sub-population, comparison of # of nodes explained with descendant and thickness correspondences: Left Comparison

The paper includes a comparison of thickness and descendant correspondence for back, left and right sub-populations:

  • Thickness Correspondence:
    1. Scatterplots of scores belonging to principal components 1, 2, 3 and 4: Back, Left and Right
    2. Scatterplots of *cumulative* scores belonging to principal components 1, 2, 3 and 4: Back, Left and Right
    3. Scatterplots of age parameter with principal components 1, 2 and 3: Back, Left and Right
  • Descendant Correspondence:
    1. Scatterplots of scores belonging to principal components 1, 2, 3 and 4: Back, Left and Right
    2. Scatterplots of *cumulative* scores belonging to principal components 1, 2, 3 and 4: Back, Left and Right
    3. Scatterplots of age parameter with principal components 1, 2 and 3: Back, Left and Right

Object Oriented Data Analysis: Sets of Trees.

Here are some movies for this paper: (It may take around 30 seconds to load one movie)

The complete draft of the paper with detail proofs:

  • Wang, H. and Marron, J.S. (2005) pdf
Education

B.S., Nankai University, Tianjin, China

Ph.D., University of North Carolina, Chapel Hill

Current Research Interests

Object Oriented Data Analysis

Spatial Statistics

Information Fusion

Statistical Analysis on Networks

Computational Neuroscience

Contact Information

216 Statistics Building
Department of Statistics
Colorado State University
Fort Collins, CO80523

Email: wanghn@stat.colostate.edu
Voice: 970-491-2449

Acknowlegement of Support

My research has been supported by NSF grants DMS-0706761, DMS-0854903, DMS-1106975, DMS-1521746 and DMS-1737795 as well as grants with other collaborators.