Bayesian Conditional Tensor Factorizations for High-Dimensional Classification.

Area of Science:

• Statistics
• Machine Learning
• Bioinformatics

Background:

• Categorical data analysis is crucial in fields like genomics.
• High-dimensional predictors and complex interactions pose challenges for traditional models.
• Parsimonious models and variable selection are needed for accurate classification and inference.

Purpose of the Study:

• To develop a flexible statistical model for classification with high-dimensional categorical predictors.
• To enable variable selection and the modeling of higher-order interactions.
• To provide a Bayesian computational framework for uncertainty quantification.

Main Methods:

• Utilizing a structured Tucker factorization to define conditional probabilities.
• Implementing a Markov chain Monte Carlo (MCMC) algorithm for Bayesian posterior computation.
• Leveraging near low-rank assumptions for theoretical guarantees.

Main Results:

• The proposed model can characterize any conditional probability.
• The Bayesian approach facilitates variable selection and interaction modeling.
• The posterior distribution achieves near parametric contraction rates in ultra-high dimensions.

Conclusions:

• The Tucker factorization-based Bayesian model offers a powerful approach for high-dimensional categorical data analysis.
• The method is suitable for classification tasks and identifying important predictors in complex datasets.
• Demonstrated effectiveness in simulations and biomedical applications, particularly in genomics.