Academic Presentations & Talks

🎤 Seminars & Presentations

1. Convergence of Random Series and Large Deviations

  • Context: Advanced Probability Theory Seminar
  • Date: Fall 2025
  • Duration: 120-minute lecture

Abstract & Key Topics:

Delivered an in-depth lecture focused on the rigorous, measure-theoretic foundations of limit theorems and tail events. The presentation covered the detailed proofs and applications of:

  • Tail \(\sigma\)-fields, Kolmogorov’s 0-1 Law, and the Hewitt-Savage 0-1 Law.

  • Kolmogorov’s Maximal Inequality and the Three-Series Theorem.

  • The Strong Law of Large Numbers (SLLN) under various conditions.

  • Large Deviations: Provided a rigorous proof of Cramér’s Theorem, highlighting the use of Moment Generating Functions (MGF), Legendre transforms, and the method of exponential tilting (change of measure via the Radon-Nikodym derivative) to bound tail probabilities.

2. Robustness of Multiple Knockoff Methods

  • Context: Weekly Statistical Seminar (Prof. Lijun Wang’s Group)
  • Date: Fall 2025
  • Duration: 90-minute talk

Abstract & Key Topics:

Presented a comprehensive review of Model-X and derandomized knockoff procedures, emphasizing their theoretical guarantees for variable selection. The talk detailed:

  • The mechanisms of finite-sample False Discovery Rate (FDR) control and e-BH thresholding.

  • My ongoing research findings regarding the severe power breakdown (Power \(\to 0\)) of e-value-based knockoffs under extreme settings, specifically heavy-tailed noise (e.g., Cauchy distribution) and high feature collinearity.