Kernel density estimator
Definition taught in Hierarchical clustering and kernel density estimation, part of Statistical learning
Kernel density estimator
| Type | Definition |
| Taught in | Hierarchical clustering and kernel density estimation |
| Part | Statistical learning |
| Questions using it | 3 |
For a sample \{\mathbf{x}_1,\ldots,\mathbf{x}_n\} in p dimensions, take K to be a symmetric probability density and H a symmetric positive definite bandwidth matrix. The kernel density estimate is
\widehat f(\mathbf{x};H)=\frac1n\sum_{i=1}^{n}K_H(\mathbf{x}-\mathbf{x}_i), \qquad K_H(\mathbf{x})=|H|^{-1/2}K(H^{-1/2}\mathbf{x}),
with H^{-1/2} obtained from the spectral decomposition. These assumptions give a nonnegative estimate that integrates to one. More general kernel constructions exist. The formulas below use this density-kernel setting.
Used in
- Taught in Hierarchical clustering and kernel density estimation, where the derivation and examples are.
- Also used in Descriptive statistics · Statistical classifiers and discriminant analysis · Support vector machines
- Questions that use it (3) — A tempting wrong turn (answer) · Clustering and smoothing choices · Nonlinear separation of XOR (answer)
- All 6 questions on Hierarchical clustering and kernel density estimation
See also
Kernel · Kernel of a density · Gaussian kernel · Positive definite matrix · Choosing the bandwidth · Eigenvalues and eigenvectors · Epanechnikov kernel · Gram matrix