Research Projects
Please explore the following research directions, ordered progressively from foundational entry points to advanced statistical and machine learning frameworks:
01 · Foundational Entry
1. Context-Aware Aspect Polarity and Latent Semantic Clustering
Sublinear TF-IDF, Truncated SVD (LSA), & Local Aspect Window Polarity
02 · Spectral Graph Theory
2. Spectral Graph Connectivity and Spherical Representation Fusion
Graph Laplacians, Random-Walk Mixing, & Spherical Modality Fusion (TGSF)
03 · Sequence Horizons
3. Causal Renewal Ratios and Lookback Selection in Multi-Wave Time Series
Leakage-Free Renewal Ratios, Rolling-Window Overlap, & Validation Memory Selection
04 · Global Sensitivity
4. Global Sensitivity Analysis and Surrogate Input Compression
Sobol Indices, Proportional Marginal Effects (PME), & Importance-Weighted PCA
05 · Econometric & Option Features
5. Econometric Volatility Filtering and Analytical Option Sensitivities
Leakage-Free GARCH(1,1), Black-Scholes Greeks, & Martingale Benchmarks
06 · Sparse Transformers
6. ProbSparse Self-Attention and Generative Multi-Horizon Decoding
O(L ln L) Query Sparsity, Conv1D Distilling, & One-Shot Multi-Step Decoding
07 · Variational Deep Learning
7. Bayesian Recurrent Networks and Variational Uncertainty Calibration
ELBO Variational Inference, Total Variance Decomposition, & Temperature Scaling
08 · Hierarchical Bayes
8. Bayesian Conjugate Updating and Hierarchical Partial Pooling
Normal-Normal & Beta-Binomial Shrinkage, Empirical Bayes, & Fair Benchmarking
09 · State-Space MCMC
9. Bayesian State-Space Models and MCMC Error Covariance Estimation
Kalman Filtering, Riccati Steady State, Blocked FFBS, & Online Matrix-t Filtering
10 · Advanced Frontier
10. Low-Dimensional Surface Geometry and Tempered Survey Subsampling
No-Arbitrage Convex Cones, 3D Surface Manifolds, & Horvitz-Thompson Sampling
