Graduation Year
2012
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Michael Orrison
Reader 2
Weiqing Gu
Terms of Use & License Information
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
Rights Information
© Aaron Pribadi
Abstract
Techniques from representation theory (Diaconis, 1988) and algebraic geometry (Drton et al., 2008) have been applied to the statistical analysis of discrete data with log-linear models. With these ideas in mind, we discuss the selection of sparse log-linear models, especially for binary data and data on other structured sample spaces. When a sample space and its symmetry group satisfy certain conditions, we construct a natural spanning set for the space of functions on the sample space which respects the isotypic decomposition; these vectors may be used in algorithms for model selection. The construction is explicitly carried out for the case of binary data.
Recommended Citation
Pribadi, Aaron, "Algebraic Methods for Log-Linear Models" (2012). HMC Senior Theses. 41.
https://scholarship.claremont.edu/hmc_theses/41
