Bayes consistency of -nearest neighbours
Theorem taught in Nearest neighbours, part of Statistical learning
Bayes consistency of -nearest neighbours
| Type | Theorem |
| Taught in | Nearest neighbours |
| Part | Statistical learning |
In fixed-dimensional Euclidean space, the standard independent identically distributed k-nearest-neighbour rule is weakly universally consistent when k=k_n\to\infty and k_n/n\to 0, with appropriate tie handling: its expected risk approaches the Bayes risk. More neighbours reduce voting noise. A vanishing sample fraction keeps the neighbourhood local.
Used in
- Taught in Nearest neighbours, where the derivation and examples are.
- All 8 questions on Nearest neighbours
See also
Bayes classifier · Rank distance · -nearest neighbours · Distance and scale in nearest neighbours · Ties and the choice of k · Consistency and the factor of two · Laboratory: what a distance metric changes · Cover–Hart bound