Under construction. This area is a framework being built: most courses have no teaching material yet, and things may change or break. Private self-study. Not an official programme and not recognised by any ministry or school. No qualification, mark or document is issued, and “years 1 to 3” and “advanced” are names of study paths only.
E32 Kernel methods and Gaussian processes
Years 1 to 3 pathE: Proposed extensionsplannedabout 120 h (planning estimate)
Planned: syllabus only, no teaching material yet. Nothing on this page can be studied; it describes what the course would cover.
Named in: Years 1 to 3 pathway
Why this course
Kernels link functional analysis to learning; Gaussian processes are the standard tool for uncertainty.
Prerequisites
- Required
- B08 Linear algebra II: abstract structure, B11 Probability I, B13 Real analysis II: metric & multivariable analysis
- Recommended
- B17 Mathematical statistics I
- Can be taken at the same time
- none
- Everything required, transitively (12 courses)
- B01, B02, B03, B04, B05, B06, B08, B09, B11, B13, F01, F02
- Courses that require this one
- E35
Concept-level units
Units follow the syllabus order, as a recommended sequence rather than a gate.
- Positive-definite kernels and reproducing kernel Hilbert spaces
- Representer theorem
- Support vector machines and the margin
- Kernel ridge regression
- Gaussian processes: prior, posterior, covariance functions
- Hyperparameters and marginal likelihood
- Neural tangent and infinite-width connections
- Scaling to large data
Assessable outcome
Derive a kernel method from an RKHS argument and compute a Gaussian-process posterior by hand for a small case.
Assessment design
- topic exercises
- mixed problem sets
- unseen proof or derivation problems
- cumulative examination
cumulative; uses spaced retrieval
Resources
Every title here is candidate, unverified unless marked verified. Titles were suggested while planning. Nobody has checked that they exist, what they cost or how they are licensed.
- Rasmussen and Williams · Gaussian Processes for Machine Learning (free)
- Schölkopf and Smola · Learning with Kernels
- Murphy · Probabilistic Machine Learning: Advanced Topics (free)
Content record
- Version
- 0.0.0
- Review
- no review of any kind
- Provenance
- PROPOSED by the assistant on 4 Nov 2026 so that a person with a mathematics degree can read AI articles fluently; not in the owner's brief; APPROVED by the owner on 4 Nov 2026 as an elective; still needs a curriculum reviewer
- Known issues
- Approved as an elective on 4 Nov 2026; syllabus only, no lessons, candidate resources unverified, needs a curriculum reviewer.
- Type
- course
Bridges and laboratories
No bridge or laboratory is attached to this course yet.
You and this course
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