▶Kernel covariance
The kernel sets prior covariance between function values at two inputs.
Gaussian Process Regression
Predicting curves together with uncertainty
A Gaussian process places a probability distribution over functions. Conditioning on observed data produces both a posterior mean curve and location-dependent uncertainty.
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The essential idea: the kernel expresses which inputs should have similar function values.
One Concept · One Example
What to notice
- Predictions interpolate information through the kernel.
- Uncertainty contracts near observations.
- Length scale controls smoothness and range of influence.
A distribution over plausible curves
Noisy observations
Observation noise adds variance to the covariance matrix diagonal.
Shape a posterior with the kernel
Adjust length scale and observation noise. The mean and uncertainty band respond together.
GPR uses covariance structure to combine nearby observations into predictions with explicit uncertainty.