Instructor: J. S. Marron

Email: marron@unc.edu

Office: 352 Hanes Hall

Course Notes:

1.   Tuesday, 8/19/2025:  Organizational Matters, OODA Book, What is OODA?, Taste of OODA Examples (including Spanish Male Mortality, Amplitude – Phase, Shapes, Sounds, Faces), 3 Major Phases of OODA, Projections, Scatterplot Matrices, Trait by Trait Views.
2.   Thursday, 8/21/2025:  Principal Component Analysis (PCA), Object Space – Trait Space, Scree Plots, Define Modes of Variation, Prob. Dist’ns as data objects, PCA Toy & Real Examples, Shifted Parabolas Data.
3.   Tuesday, 8/26/2025:  PCA Toy & Real Examples.  Lung Cancer Data, Limitations of PCA: Apple, Banana, Pear, NCI-60 Data.
4.   Thursday, 8/28/2025:  Inference using DiProPerm, OODA Terminology, Marginal Distribution Plots.
5.   Tuesday, 9/2/2025:  Marginal Distribution Plot Analysis of Drug Discovery Data, Normalization and Correlation PCA, Transformations, Melanoma Data.
6.   Thursday, 9/4/2025:  Automatic Shifted Log Transformation, ROC Curve to Quantify Impact of Transformation on Gene Expression Data, Heatmap Data Visualization, Other Directions for Scatterplot Views, Centering.
7.   Tuesday, 9/9/2025: Details of PCA, Review Linear Algebra, Covariance Matrices, PCA as Optimization, Alternate Viewpoints of PCA (Data Representation, Distribution of Energy).
8.   Thursday, 9/11/2025:  More Viewpoints of PCA (Simulation, Comparison to SVD), Alternate Relationship Measures, Data Integration, Revisit Centering.  Coleman Ferrell: Relationship Between Concussions and Symptoms
9.   Tuesday, 9/16/2025:  Finish Centering Discussion, Partial Least Squares, Canonical Correlation Analysis, Angle Based Joint and Individual Variation Explained (AJIVE).
10.   Thursday, 9/18/2025:  FMRI Data, AJIVE Algorithm and Diagnostics.  Ishita Pethkar: Extension of GRIDY
11.   Tuesday, 9/23/2025:  Breast Cancer Images and Genomics, Multiple Genomics in Breast Cancer, Amplification Adjustment in Single Cell RNAseq.
12.   Thursday, 9/25/2025:  Data Integration Via Analysis of Subspaces  (DIVAS).  Yang Liu: Introduction to Targeted Learning
13.   Tuesday, 9/30/2025:  DIVAS, DIVAS Toy Example, DIVAS analysis of TCGA & Mortality Data, Distance Methods: Fre’chet Mean and Median.
14.   Thursday, 10/2/2025:  Distance Methods: Multi-Dimensional Scaling (~PCA), Shapes as Data Objects, Shape Representations (Landmark, Boundary, Shape).  HyungGyu Min:  Finding Gene Program Using Consensus NMF
15.   Tuesday, 10/7/2025:  UNC Well Being Day (no class)
16.   Thursday, 10/9/2025:  Male Pelvis Data, Manifold Data, Directional Data, S-rep Analysis, Principal Geodesic Analysis.  Max van Fleet: Dimension Reduction of PDAL data
17.   Tuesday, 10/14/2025:  Principal Nested Spheres, Polysphere PCA, Scaled Torus PCA, Nonnegative Nested Cone Analysis Principal Curves and Surfaces, General Motivation for Backwards Methods.
18.   Thursday, 10/16/2025:  UNC Fall Break (no class)
19.   Tuesday, 10/21/2025:  Backwards PCA, Principal Curves and Surfaces, General Motivation for Backwards Methods.  Zhen Fang:  Conformal Inference for Individual Treatment Effects
20.   Thursday, 10/23/2025:  Curve Registration, Shifted Betas Example, Amplitude and Phase Modes of Variation, Fisher-Rao Modes of Variation.
21.   Tuesday, 10/28/2025:  Fisher-Rao Modes of Variation, Total Ion Count Data, Principal Nested Spheres on SRVF Sphere,  Juggling Data.  Dev Ghandi: Predicting Patterns of Occurrence of PFAS in Water in the United States Using Machine Learning
22.   Thursday, 10/30/2025:  High Dimension Low Sample Size Asymptotics,  David Allemang: Protrusions on Skeletal Shape Representations
23.   Tuesday, 11/4/2025:  High Dimension Low Sample Size Asymptotics, Random Matrix Theory,  Will Nenad: Shape analysis of Breast Tumors
24.   Thursday, 11/6/2025:  K-means Clustering, Hierarchical Clustering,  Erin Ishikawa: A Survey on the Hierarchical Nuclear Norm
25.   Tuesday, 11/11/2025:  SigClust, Smoothing:  Srujay Patelu: Big Data / Ethnography
26.   Thursday, 11/13/2025:  Smoothing, SiZer:  Ruiduo Jia: CosMX Data Analysis from 5 Samples
27.   Tuesday, 11/18/2025:  Topological Data Analysis (Andrew Walker).
28.   Thursday, 11/20/2025:  SiZer, Classification (Discrimination) basics, Linear Discriminant Analysis (Non-parametric derivation),  Yikai Wang: Breast Cancer Image Classification
29.   Tuesday, 11/25/2025:  Likelihood derivation of Linear Discriminant Analysis, Kernel Classification, Support Vector Machines
30.   Thursday, 11/27/2025:  UNC Thanksgiving (no class)
31.   Tuesday, 12/2/2025:  Distance Weighted Discrimination, HDLSS Batch Adjustment

References:

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Carmichael, I., & Marron, J. S. (2021). Geometric insights into support vector machine behavior using the KKT conditions. Electronic Journal of Statistics, 15(2), 6311-6343 (cited 11/25/25, 12/2/25)

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Chaudhuri, P., & Marron, J. S. (2000). Scale space view of curve estimation. Annals of Statistics, 408-428 (cited 11/20/25)

Chen, M., & Zhou, X. (2016). Single Cell Partial Least Squares, unpublished manuscript (cited 9/19/25)

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Dai, W., & Genton, M. G. (2017). Multivariate Functional Data Visualization and Outlier Detection. arXiv preprint arXiv:1703.06419. (cited 11/13/25)

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Hannig, J., & Marron, J. S. (2006). Advanced distribution theory for SiZer. Journal of the American Statistical Association, 101(474), 484-499 (cited 11/20/25)

Hannig, J., Marron, J. S., & Riedi, R. (2001). Zooming statistics: Inference across scales. Journal of the Korean Statistical Society, 30(2), 327-345 (cited 11/13/25)

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Jung, S., Foskey, M., & Marron, J. S. (2011). Principal arc analysis on direct product manifolds. The Annals of Applied Statistics, 578-603 (cited 10/14/25)

Jung, S., Dryden I. L., & Marron, J. S., (2012) Analysis of Principal Nested Spheres, Biometrika, doi: 10.1093/biomet/ass022 (cited 10/14/25)

Jung, S., Sen, A. and Marron, J. S. (2012), Boundary behavior in high dimension, low sample size asymptotics of PCA, The Journal of Multivariate Analysis,109, 190–203 (cited 11/4/25)

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Keefe, T. H., & Marron, J. S. (2025). Powerful significance testing for unbalanced clusters. Journal of Computational and Graphical Statistics, 1-13 (cited 11/11/25)

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Kimes, P. K., Cabanski, C. R., Wilkerson, M. D., Zhao, N., Johnson, A. R., Perou, C. M., Makowski, L., Marron, J. S. & Hayes, D. N. (2014) SigFuge: single gene clustering of RNA-seq reveals differential isoform usage among cancer samples, Nucleic Acids Research (2014): gku521 (cited 8/26/25)

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