- Abstract:
- Consider a random function f with a separable (or tensor product) covariance function, i.e. where x is broken in D groups (x^1, x^2, ..., x^D) and the covariance function has the form k(x, tilde{x}) = \prod_{i=1}^D k^i(x^i, tilde{x}^i). We also require that observations of f are made on a D-dimensional grid. We show how conditional independences for the Gaussian process prediction for f(x_*) (corresponding to an off-grid test input x_*) depend on how x_* matches the observation grids. This generalizes results on autokrigeability (see, e.g. Wackernagel 1998, ch. 25) to D > 2.
- Copyright:
- 2007 by the University of Edinburgh.
- Links To Paper
- Chris Williams' online publications
- Bibtex format
- @Misc{EDI-INF-RR-1228,
- author = {
Chris Williams
and Mac Baran
and Edwin Bonilla
},
- title = {A Note on Noise-free Gaussian Process Prediction with Separable Covariance Functions and Grid Designs},
- year = 2007,
- month = {Dec},
- url = {http://www.dai.ed.ac.uk/homes/ckiw/postscript/KroneckerDec07.pdf},
- }
|
