Andreas Buja's Home Page

Doctoral Program in Statistics:
If you are interested in our Ph.D. program, please, visit our program website.
Once you decide to apply, start your application at this website.

Current Interests:

• Recommender Systems:
  In his Ph.D. thesis, Dan Fleder devised a scheme whereby observational data about consumers of music before and after joining a recommender service could be interpreted as describing a natural experiment. As a consequence, he got as close as conceivable to causal inference about the effects of recommender systems on consumers in a particular setting. Here is a short version in Knowledge@Wharton: Different Worlds: Do Recommender Systems Fragment Consumers' Interest?

• Statistical Inference after Model Selection:
  • Valid Post-Selection Inference by Richard Berk, Lawrence Brown, Andreas Buja, Kai Zhang and Linda Zhao.
    When predictors for statistical models are selected by looking at the data, statistical inference based on these models is in danger of being invalid. We show that confidence intervals may need to be widened considerably to protect against invalidation. This is a fundamental difficulty with statistical inference that has implication all the way down to how we teach statistics in introductory courses.

• Visualization of Large Correlation Tables:
  • A Tool for Mining Large Correlation Tables: 'Association Navigator'
    This is a report (joint with Abba Krieger and Ed George) written for the Simons Foundation - Autism Research Initiative (SFARI). The work under a SFARI grant was the reason why we created an interactive tool for visualizing correlation tables for many hundreds of variables. The report draws its examples from the 'Simons Simplex Collection' (SSC), a large database of autism phenotype data.
  • The Association Navigator software, written in the R language (currently only for MS Windows). You can load the software into an R interpreter by executing the following expression:
    source("http://stat.wharton.upenn.edu/~buja/association-navigator.R")
    Then follow the simple instructions on page 35 of the above report to apply the software to your own numeric data matrix.

• Multidimensional Scaling:
  • Lisha Chen's thesis paper, which resulted in the following two articles
  • Energy/Stress Functions for Dimension Reduction and Graph Drawing: Power Laws and Their Clustering Properties (Chen and Buja; 2009, conditionally accepted by JMLR) [.pdf]
  • Local Multidimensional Scaling for Nonlinear Dimension Reduction, Graph Drawing and Proximity Analysis (Chen and Buja; JASA 2009) [.pdf]
  • Data Visualization With Multidimensional Scaling (Buja, Swayne, Littman, Dean, Hofman and Chen; JCGS 2008) [.pdf]
  • Visualization Methodology for Multidimensional Scaling (Buja and Swayne; JoC 2002) [.pdf]

• Penalized Singular Value Decompositions with Jianhua Huang and Haipeng Shen:
  • The Analysis of Two-Way Functional Data Using Two-Way Regularized Singular Value Decompositions (Huang, Shen and Buja, JASA, 2009) [.pdf], with supplementary material [.pdf]
  • Functional principal components analysis via penalized rank one approximation (Huang, Shen and Buja; Electronic Journal of Statistics, 2008)[.pdf]

• Inference for EDA and Diagnostics: One would think that the graphical methods of exploratory data analysis and model diagnostics are beyond, and even adverse to, statistical inference. This is not so. With some simple protocols it is possible to assign p-values to visual discoveries.
  • "Statistical inference for exploratory data analysis and model diagnostics" [pdf] with supplementary materials [pdf] (Buja, Cook, Hofmann, Lawrence, Lee, Swayne, Wickham, 2009; Philosophical Transactions of The Royal Society, A)
  • A precursor talk given at the Joint Statistics Meetings 1999, with Di Cook [.pdf].
  • A related topic is model checking with parametric bootstrap: I brought this up back in 2004 in a discussion of a paper by Andrew Gelman who does the same with a posterior predictive approach.
    Here are Gelman's JCGS article, followed by my discussion, and his rejoinder.

• Two papers on special topics in high-dimensional data visualization, joint with Di Cook, Dan Asimov, and Catherine Hurley:
  • Theory of Dynamic Projections in High-Dimensional Data Visualization [pdf] (accepted by EJS (``Electronic Journal of Statistics''). Describes the invariant Riemannian geometries on Stiefel manifolds.
  • Computational Methods for High-Dimensional Rotations in Data Visualization [pdf]
    Appeared in "Handbook of Statistics" (eds. E. Wegman, C. R. Rao; 2005).
  An older version that had both papers in one should be considered out of date.

• Multivariate Analysis: A talk I gave at an econometrics workshop at Stanford. It tries to answer the question of how to choose the ``reference metric'' or the constraint in multivariate methods based on eigendecompositions. [.pdf]

• On a topic in marketing, joint with N. Eyuboglu:
  Quasi-Darwinian Selection in Marketing Relationships [.pdf]
  Journal of Marketing, Oct 2007, featured JM blog article and a finalist for JM's 2007 Harold H. Maynard Award.
  Along with the paper go a few scenario calculations that are not included in the article: [.pdf]

• Here is a paper that started out as work on boosting but turned into something different, joint with Werner Stuetzle and Yi Shen:
  Loss Functions for Binary Class Probability Estimation: Structure and Applications. (Former title: Degrees of Boosting) [.pdf] (under revision)
  Yi Shen's 2005 Ph.D. thesis on cost-weighted class probability estimation [pdf]

• On a simple modification of boosting, joint with David Mease and Adi Wyner:
  Cost-Weighted Boosting with Jittering and Over/Under-Sampling: JOUS-Boost [pdf]
  (Journal of Machine Learning Research 8 (Mar), 409-439, 2007)

• A paper on bagging, joint with Werner Stuetzle:
  Observations on Bagging (Statistica Sinica 2006, Special Issue on Machine Learning, 16 (2), 323--352 (2006)) [pdf]

  A preliminary version and a companion paper which I keep posted because others have started referring to them:
  The Effect of Bagging on Variance, Bias, and Mean Squared Error [.pdf] PPT slides,
  Smoothing Effects of Bagging [.pdf]

• A paper on the use of simulation for simultaneous inference, with Wolfgang Rolke:
  Calibration for Simultaneity: (Re)Sampling Methods for Simultaneous Inference with Applications to Function Estimation and Functional Data [.pdf, 1.7MB] (under revision)

• Visual Comparison of Datasets using Mixture Decompositions [.pdf]
  Alan Gous and Andreas Buja; Journal of Computational and Graphical Statistics, 13 (1), 1-19 (2004).
  (We are permitted to post the color version of this paper. The printed version is b/w with gray-scale figures.)

• A paper on classification and regression trees with a datamining orientation:
  Data Mining Criteria for Tree-Based Regression and Classification [.ps.gz]
  A. Buja and Y.-S. Lee; Proceedings of KDD 2001, 27--36.