research note in progress
Stochastic Optimization Notes
A working set of notes on stochastic approximation, noisy gradients, convergence intuition, and how optimization theory connects to modern ML practice.
Notes / Writing
Research notes and technical archive.
These are research notes in progress and selected presentation topics from my preparation in applied mathematics, machine learning, scientific computing, stochastic optimization, graph learning, and robust state-space estimation. The notes emphasize derivation, geometric intuition, computational experiments, and failure cases. Draft status is visible so the page does not imply finished papers or formal publications.
working outline
Mirror Descent and Momentum Methods
Notes on geometry, regularization, momentum, adaptive methods, and the mathematical intuition behind iterative optimization algorithms.
working outline
Diffusion Models and ML Foundations
A bridge between generative modeling, stochastic processes, denoising objectives, and the computational details that make diffusion systems trainable.
working outline
Gaussian Processes with Derivative Matching
Notes on probabilistic modeling, derivative observations, covariance structure, and how smoothness assumptions enter model behavior.
polished outline
Robust Kalman Filtering
A research note outline on stochastic filtering, covariance misspecification, asynchronous measurements, outliers, and simulation-based robustness testing.
working outline
Foundations of Stochastic Control
Notes connecting dynamic systems, uncertainty, control objectives, value functions, and the mathematical language behind sequential decision-making.
research note in progress
Numerical Linear Algebra Notes
Notes on spectral structure, conditioning, matrix factorizations, iterative methods, and numerical behavior in large-scale ML computations.
Draft not yet public
working outline
Graph Learning Notes
Notes on graph-structured data, road-network topology, message passing, spectral graph ideas, retrieval, and representation learning.
Selected Presentations
Talks and technical walkthroughs.
Presentation materials are listed as archive topics unless a public artifact is ready to share.
- Diffusion models
- Derivative-matching Gaussian processes
- Robust Kalman filtering
- Stochastic control
- SGD, momentum, and Adam
- Mirror descent
- Graph neural networks for risk modeling
- Benchmark design for LLM evaluation
- Calibration and uncertainty for biomedical ML