Research

Our group explores the intersection of statistical methods, machine learning, and human cognition, with projects spanning financial data analysis, large language model (LLM) reasoning, and neuroscience.

1. Financial Data Analysis

Financial markets are dynamic, noisy, and information-rich, making them an ideal testbed for statistical modeling and machine learning. Our research focuses on two complementary aspects:

  • Engineering Predictive Models – We design and implement predictive algorithms and evaluate their performance in real-time markets (e.g., stock, cryptocurrency, and currency exchange).
  • Theoretical Foundations – We study portfolio optimization, information aggregation, and risk management under uncertainty, with recent interest in applying large language models (LLMs) to financial news and unstructured data.

2. Reasoning with Large Language Models (LLMs)

LLMs have shown remarkable success in natural language processing, but their reasoning ability remains an open challenge. We investigate both the limits and possibilities of LLM reasoning. Some active challenge topics include:

  • Multi-step reasoning and chain-of-thought robustness
  • Commonsense reasoning under uncertainty
  • Mathematical reasoning and symbolic manipulation
  • Causal reasoning and counterfactual inference
  • Generalization across tasks and domains
  • Robustness to adversarial prompts and misleading information
  • Combining LLMs with external tools (e.g., knowledge graph, tools, simulations) to extend reasoning capability

3. Human Cognition and Brain Research

Our third research area focuses on understanding and training the human brain. We study how the brain adapts to new and challenging tasks (e.g., learning mathematics), and how to strengthen cognitive resilience against adverse factors such as aging and substance use.

This work is mainly supported by the NIH (e.g., MH118927, AG066970, R25DA058940) and includes:

  • Developing geometry-based methods for brain connectome analysis
  • Advancing structural connectome estimation in aging populations
  • Exploring ANS-based personalized cognitive training interventions
  • Promoting collaborative research on connectome analysis for substance use disorders