Trajectory ML 01: From Observations to Hidden State
A shared framework for cell differentiation and character conversations, with a reproducible synthetic project and an honest distinction between geometry and time.
Machine Learning
Trajectory ML 09: Learn where a state moves next
Estimate a velocity field from paired observations, then discover why predicting one step and rolling out a trajectory are different tests.
Trajectory ML 10: Move a population with optimal transport
Infer a mass-preserving coupling between snapshots, distinguish it from tracked identity, and implement Sinkhorn transport.
Trajectory ML 11: Continuous dynamics and flow matching
Connect neural vector fields, ODEs, SDEs, and flow matching without confusing generated paths with observed temporal mechanisms.
Trajectory ML 12: Outcomes, survival, and causal questions
Predict outcomes without future leakage, handle censored follow-up, and distinguish forecasting from the effect of an intervention.
Trajectory ML: A Twelve-Lesson Course and Shared Lab
Recovering hidden states and trajectories from observations, from PCA to Flow Matching, survival analysis and causality, with one synthetic dataset.
MacKay's Information Theory: The Free Book and the Lectures
David MacKay’s classic ties information theory, inference, and machine learning into one story, and both the book and the lecture videos are free. Where to get them, to open this series.
K-means, GMM, EM: Three Nested Russian Dolls of Clustering
K-means is actually an extreme case of GMM, and GMM is the canonical application of the EM algorithm. How these three connect within a single framework, and how information geometry explains the relationship.
Information Geometry: How AI Learns Most Efficiently
Just as Newton’s F=ma describes the physical world, information geometry describes how AI learns. An intuitive guide for beginners.