Research

1. Bayesian Inference of Transition Diagnostic Classification Models with Multilevel Effects Using Gibbs Sampling with Pólya-Gamma Augmentation

Lan Tao, Hao Duan, Minjeong Jeon
In preparation, 2025

We develop a Bayesian framework for modeling student progression within a longitudinal diagnostic classification model. The method incorporates multilevel covariates and uses Gibbs sampling with Pólya-Gamma augmentation for efficient posterior inference.

2. Discriminative Estimation of Total Variation Distance: A Fidelity Auditor for Generative Data

Lan Tao, Shirong Xu, Chi-Hua Wang, Namjoon Suh, Guang Cheng
Preprint, 2024
arXiv:2405.15337

We propose a discriminative approach to estimate the Total Variation (TV) distance as a fidelity measure for generative models. We frame the TV distance as the Bayes risk in a binary classification setting and apply it to evaluate image data generated by GANs.

3. Injective Δ + 2 Coloring of Planar Graph Without Short Cycles

Ying Chen, Lan Tao, Li Zhang
Acta Mathematicae Applicatae Sinica (English Series), 2023
Springer Link

This paper investigates the injective coloring problem in planar graphs with girth constraints. We design new discharging rules and improve the upper bounds on injective chromatic numbers for planar graphs without short cycles.