Twelve undergraduate lessons connecting cell states and character conversations, with one synthetic dataset and executable Python labs.
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.
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.
Trajectory ML 02: PCA as the First Latent Space
Derive PCA from reconstruction and variance, connect covariance eigenvectors to SVD, and evaluate compression on unseen sessions.
Trajectory ML 03: Autoencoders, VAEs, and Useful State
Train an autoencoder and a VAE, derive the meaning of the ELBO, and separate reconstruction quality from semantic state recovery.
Trajectory ML 04: Neighborhoods, Manifolds, and the Swiss Roll
Build a neighborhood graph, understand Isomap and UMAP, and learn why a two-dimensional map is neither a clock nor a faithful atlas of global distances.
Trajectory ML 5: Diffusion Maps and Spectral Geometry
Turn local neighbors into a reversible random walk, then use its slow modes to describe global geometry.
Trajectory ML 6: Clusters, Communities, and Useful States
Compare geometric and graph partitions, then learn why a discovered cluster is a hypothesis about state.
Trajectory ML 7: From Points to Paths and Branches
Build a minimal tree baseline, understand principal curves and PAGA, and identify what pseudotime can and cannot measure.
Trajectory ML 8: Markov Models, HMMs, and State Space Models
Use observed sequence order to estimate transitions, infer hidden states, and separate filtering from smoothing.
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.