Model uncertainty

Who this path is for

Learners who want to move beyond a point prediction and explain assumptions and uncertainty.

Preparation

Shared foundations and probability

Your first useful artifact

An exact Bayesian regression posterior checked against an independent host calculation.

How to study

Start with distributions and the exact regression posterior so you have a reference for approximate inference. Run multiple HMC chains and deliberately inspect an unstable sampler before studying variational inference. Compare latent uncertainty with uncertainty in a future observation. Complete the Bayesian project with a changed prior and held-out data before moving to an optional NumPyro model.

Course phases and lessons

1. Setup & first steps

   Run a saved program and explain its environment, array output and device placement. Start on one CPU, practice sharding on four logical CPU devices, and learn how to get a TPU running, launch a TPU job, and run course experiments on TPU in parallel from Phase 00 onward.

   • Set up your learning workspace
   • Meet your arrays and devices
   • Practice with four virtual CPU devices
   • Move your experiment to a TPU
2. Arrays & pure functions

   Treat every axis as part of a contract. Work through normalization, broadcasting and immutable updates, then diagnose mistakes that still return plausible numbers.

   • From NumPy to jax.numpy
   • Shapes, broadcasting, and dtypes
   • Pure functions and explicit inputs
   • Immutable updates and indexing
3. JAX transformations

   Begin with a scalar function, then differentiate it, batch it and compile it. Compare each transformed result with a simple reference so you can explain what changed.

   • Your first gradient
   • Losses and value_and_grad
   • Batch a function with vmap
   • Compile a function with jit
   • Tracing, static arguments, and recompilation
4. State, randomness & control flow

   Make randomness, parameters and loop state explicit. Learn how to repeat an experiment without accidentally reusing randomness or mutating a caller’s state.

   • Random keys without surprises
   • Pytrees and structured parameters
   • Compiled loops with lax.scan
   • Branches with lax.cond
5. Math & optimization

   Connect geometry and probability to the updates in a training loop. Begin with linear algebra, gradient checks and gradient descent, then investigate conditioning, curvature, likelihoods, regularization and optimizer behavior.

   • Vectors, norms, and projections
   • Linear algebra and loss intuition
   • Least squares, rank, and conditioning
   • The chain rule, Jacobians, and directions
   • Gradient checking and numerical accuracy
   • Curvature, Hessians, and learning rates
   • Write gradient descent yourself
   • Probability, likelihood, and stable losses
   • Regularization and honest validation
   • Minibatches, expectation, and gradient noise
   • Optimize with Optax
   • Adam, clipping, and learning-rate schedules
6. Probabilistic modeling

   Specify probability models, derive exact Bayesian regression, implement and diagnose HMC, and compare variational approximations with predictive evidence.

   • Distributions and sampling
   • Build a Bayesian regression
   • Hamiltonian Monte Carlo and sampler diagnostics
   • Variational inference and model checking

Audit a Bayesian regression model

A guided project is available for this route.

Defend the prior and likelihood, verify posterior and sampler calculations independently, distinguish latent and observation uncertainty, and diagnose changed-condition predictive failures.

• Prior, likelihood and posterior calculations checked against an independent reference
• Multiple seeded chains with trace, acceptance and between-chain diagnostics
• Predictive intervals separating latent and observation variance, including a model-mismatch example

Read the portfolio project guide

Work through the synthesis assessment

Use this path in your learning workspace