A Study Roadmap for Uncertainty Quantification + Inverse Dynamics
This is the companion to my concept review of uncertainty quantification and inverse dynamics — a study plan for actually learning the material. The aim is a path from the Bayesian fundamentals up to physics-informed, uncertainty-aware inverse dynamic models, using sources that are free to access. I have grouped it into three levels and then sequenced it into a ten-week curriculum.
The one idea everything rests on
Before any specific method, it helps to internalize the Bayesian view, because every UQ technique is a way of approximating it. A Bayesian model treats its parameters not as single values but as a distribution, and updates that distribution as data arrives:
\[\underbrace{p(\theta \mid D)}_{\text{posterior}} \;\propto\; \underbrace{p(D \mid \theta)}_{\text{likelihood}} \;\times\; \underbrace{p(\theta)}_{\text{prior}}.\]In words: belief after seeing the data = evidence from the data × belief before. MC Dropout, Deep Ensembles, and Gaussian Processes are all different ways of approximating that posterior when computing it exactly is intractable.
Level 1 — Foundations
Start with the lay of the land and the core probabilistic machinery.
- A Review of Uncertainty Quantification in Deep Learning — Abdar et al. (2021), arXiv:2011.06225. The survey to read first; it maps the whole UQ landscape.
- A Survey on UQ Methods for Deep Learning — He & Jiang (2024), arXiv:2302.13425. Organizes methods by the source of uncertainty (data vs. model) and connects to active learning and RL.
- Gaussian Processes for Machine Learning — Rasmussen & Williams (MIT Press, 2006), free PDF at gaussianprocess.org/gpml. The standard GP text; chapters 1–2 (regression) and 5 (model selection) are the priority.
Level 2 — Core papers
These four define the methods you will actually use.
- Dropout as a Bayesian Approximation — Gal & Ghahramani, ICML 2016, arXiv:1506.02142. Proves that a dropout network approximates Bayesian inference in a Gaussian process — the theoretical basis for MC Dropout.
- A Gentle Introduction to Conformal Prediction — Angelopoulos & Bates (2021/2023), arXiv:2107.07511. Distribution-free coverage guarantees that apply to any model, with code and worked examples.
- PILCO: Data-Efficient Learning in Robotics and Control — Deisenroth & Rasmussen, PAMI 2015. The textbook treatment of a GP dynamics model with uncertainty propagation.
- BatchBALD — Kirsch et al., NeurIPS 2019, arXiv:1906.08158. Extends BALD active learning to diverse batches; PyTorch code is public.
For the inverse-dynamics-specific thread, two recent works connect directly to the research directions in the companion post:
- A Black-Box Physics-Informed Estimator based on GP Regression for Robot Inverse Dynamics — Giacomuzzo et al. (2023), arXiv:2310.06585.
- Efficient Learning of Inverse Dynamics Models for Adaptive Control — Jorge & Mistry (2022), arXiv:2205.04796. Sparse variational GP for online IDM uncertainty on a 7-DOF arm.
Level 3 — Tutorials and lectures
For implementation and a faster visual overview:
- Active Learning for Deep Learning — Jacob Gil’s blog: BALD/BatchBALD with PyTorch code, the most approachable hands-on resource.
- Conformal Prediction lecture notes — Ryan Tibshirani, UC Berkeley (2023): a rigorous, math-first complement to the Angelopoulos tutorial.
- Uncertainty Quantification in Deep Learning — Franchi, ECCV 2024 tutorial slides: a visual, end-to-end overview of modern UQ methods.
A 10-week curriculum
| Weeks | Focus | Primary material |
|---|---|---|
| 1–2 | Survey the UQ landscape; method types and uncertainty sources | Abdar et al. survey |
| 3–4 | MC Dropout and the Bayesian deep-learning view | Gal & Ghahramani + ECCV 2024 slides |
| 5–6 | Gaussian processes, then GP dynamics via PILCO | Rasmussen & Williams ch. 1–2 + PILCO |
| 7 | Conformal prediction theory, then run the code | Angelopoulos & Bates |
| 8 | BALD / BatchBALD theory, then run the GitHub code | BatchBALD + PyTorch_BatchBALD |
| 9–10 | Physics-informed GP IDM — connect to the research plan | Giacomuzzo et al. + Jorge & Mistry |
The through-line is the same as the concept review: build up to a model that reports not just a prediction but how much to trust it, then put that uncertainty to work in control. If you only have time for three things, read the Abdar survey, the Gal & Ghahramani paper, and the Angelopoulos conformal-prediction tutorial — they cover the map, the workhorse method, and the guarantee.