Research

Each line of work with its papers, numbered as on the Publications page.

Optimal Multiple Testing

Characterizing and computing the most powerful tests under exact family-wise error rate (FWER) control. By describing the error-rate constraints in closed form through elementary symmetric polynomials, an intractable combinatorial problem becomes a fast, scalable algorithm with provable linear convergence. The same approach extends to block-structured multiplicity (BOOST) and strong-FWER guarantees.

Papers
  1. BOOST: Power-Optimal Strong-FWER Testing for Block-Structured Multiplicity
  2. Most Powerful Tests with Exact Family-Wise Error Rate Control: Necessary Conditions and Fast Computation for General K
  3. Most Powerful Test with Exact Family-Wise Error Rate Control: Necessary Conditions and a Path to Fast Computing

Federated and Communication-Constrained Learning

Statistical learning and inference when data and models are distributed across nodes and communication is the bottleneck. This includes federated probe-logit distillation with matching minimax rates and optimal bandwidth allocation, and anytime-valid conformal prediction that gives distribution-free coverage guarantees for federated language models and retrieval-augmented generation (RAG) across LLM swarms, making bandwidth a first-class statistical parameter.

Papers
  1. Byzantine-Robust Federated RAG via Aligned Calibration and Fixed-Membership Conformal Prediction
  2. Matching Rates and Optimal Allocation for Federated Probe-Logit Distillation under Heterogeneous Bandwidth Budgets
  3. Certified Adaptive Refresh: Anytime-Valid Monitoring for Federated Conformal RAG
  4. Federated Language Models Under Bandwidth Budgets: Distillation Rates and Conformal Coverage

Federated and Anytime-Valid Multiple Testing

Where the two threads above meet: error control that stays valid when evidence is federated across sites that cannot pool raw data, or accumulates sequentially over time (anytime-valid, e-process-based). A central question in the federated case is how much each site must report for the guarantee to survive aggregation.

Papers
  1. Pooling Sequential Evidence Across Hypotheses: Rate-Optimal Multiple Testing at a Fixed Horizon
  2. Federated Multiple Testing with Quantized p-Values under Family-Wise Error Control

Statistical Machine Learning

Broader methodological and theoretical questions in modern machine learning: from generalization bounds for compressed and pruned neural networks to LLM-powered functional data analysis for anomaly detection in sparse, longitudinal text.

Papers
  1. LLmFPCA-detect: LLM-powered Multivariate Functional PCA for Anomaly Detection in Sparse Longitudinal Texts
  2. Generalization Bounds for Magnitude-Based Pruning via Sparse Matrix Sketching