Trajectory ML

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: 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.