Advanced Statistical Science Research Project

1. Research Topics and Objectives

Modern statistical research explores both traditional theories and contemporary applications. Key topics include:

High-Dimensional Statistics and Sparse Modeling: Sparse regression, dimensionality reduction, and model interpretability, applied in genomics, image processing, and finance.

Generative Models: Techniques such as Variational Autoencoders (VAE), Generative Adversarial Networks (GAN), and Diffusion Models for data generation, augmentation, and denoising.

Bayesian Deep Learning: Combining Bayesian inference with neural networks to improve uncertainty quantification, with applications in medical diagnosis and autonomous driving.

Causal Inference: Methods like Instrumental Variables (IV), Causal Graphs, and Deep Causal Inference (DeepIV) for identifying causal relationships beyond correlation.

Time Series Analysis and Reinforcement Learning: Using Bayesian dynamic modeling and reinforcement learning for financial trading and energy management.

Self-Supervised Learning: Extracting representations from unlabeled data through methods like SimCLR and BYOL.

Research Objectives

Develop efficient statistical learning models for improved predictive accuracy and computational efficiency.

Design interpretable AI techniques to enhance trust in data-driven decision-making.

Explore statistical applications in bioinformatics, financial technology, and computational social sciences.

2. Research Methods

High-Dimensional Statistics and Sparse Modeling

LASSO / Elastic Net: Variable selection and multicollinearity reduction in high-dimensional data.

Graphical Lasso: Sparse covariance matrix estimation for network analysis.

PCA & NMF: Dimensionality reduction and pattern discovery.

Random Matrix Theory: Studying statistical properties of large-scale data.

Bayesian Statistics and Probabilistic Graphical Models

MCMC Methods: Metropolis-Hastings and Gibbs Sampling for efficient Bayesian inference.

Variational Inference (VI): Applied in high-dimensional Bayesian models for NLP and computational biology.

Causal Inference

Classical Methods: Propensity Score Matching (PSM), Instrumental Variables (IV), and Difference-in-Differences (DiD).

Deep Learning-Based Methods: CausalGAN and Causal Variational Autoencoders (CausalVAE).

Modern Machine Learning and Statistical Learning

Ensemble Learning:
Random Forest, Gradient Boosting Trees (XGBoost, LightGBM).

Bayesian Optimization for hyperparameter tuning.

Deep Learning:
Self-Supervised Learning (SimCLR, MoCo, BYOL).

Graph Neural Networks (GNNs) for structured data analysis.

Diffusion Models for image generation and denoising.

Time Series Analysis and Reinforcement Learning

State-Space Models: Kalman Filter, Particle Filter.

Long-Term Dependency Modeling: LSTM, Transformer-based models (e.g., TimeGPT).

Reinforcement Learning (RL):
Deep RL (Deep Q-Learning, PPO) for financial trading and robotics.

Causal RL for policy learning with causal inference.