This book is about the mathematical foundations of data science. 1. Introduction 2. Curses, Blessings, and Surprises in High Dimensions 3. Singular Value Decomposition and Principal Component Analysis 4. Linear Regression and Regularization 5. Graphs, Networks, and Clustering 6. Nonlinear Dimension Reduction and Diffusion Maps 7. Linear Dimension Reduction via Random Projections 8. Optimization for Data Science 9. Classification 10. A Mathematical Introduction to Deep Learning 11. Large Sample Limit of Graph Laplacians 12. Community 13. Concentration of Measure and Gaussian Analysis 14. Matrix Concentration Inequalities 15. Compressive Sensing and Sparsity 16. Low-Rank Matrix Recovery
Bayesian optimization (BO) is an optimization method that sequentially proposes the next candidate explainable variables for optimizing target variables by balancing exploration and exploitation. BO is often used under a limited evaluation budget, such as hyperparameter tuning of…
Convolutional neural networks (CNNs) are widely used for time-series classification, but their deployment in critical domains requires understanding the temporal and spectral patterns that drive their predictions. Concept extraction (CE) methods identify such patterns by analyzin…
Reinforcement learning with verifiable rewards (RLVR) broadcasts a single response-level reward to every token, while on-policy distillation (OPD) scores each token against a stronger teacher for a dense advantage but caps performance at teacher quality and discourages exploratio…
Synthetic face datasets are increasingly used to reduce privacy exposure and data access constraints in biometric recognition. Yet the generators that produce these datasets are trained on real faces, so synthetic data may still reveal their real source data. We study this risk t…
Large-scale multivariate time series from heterogeneous IoT sensors demand accurate long-term forecasting for resource scheduling and predictive maintenance. While recent time series foundation models exhibit strong generalization, they rely on static parametric knowledge and lac…
Balancing sequence length, representational capacity, and long-horizon stability is a central problem in autoregressive (AR) speech and audio generation. Representations with higher frame rates or greater capacity can preserve more signal detail, but they also make streaming gene…