Squared exponential kernel
A squared exponential kernel is a similarity or covariance function whose value decreases exponentially as the squared distance between inputs increases.
Experimentation for Engineers
The squared exponential kernel is a Gaussian-process covariance function whose similarity decreases exponentially with squared input distance.
- How it is used
- Supports Gaussian process regression for estimating CPU time and other business metrics between measured parameter values.
- How deep it goes
- Explains weighting, length-scale selection, clustered observations, kernel matrices, and relative uncertainty, but not hyperparameter selection in depth.
- Examples
- Uses NumPy snippets, two CPU-time measurements, plotted regression curves, clustered observations, and four independent regression examples.
- What you can do after
- Apply it via NumPy to construct smooth GPR estimates and relative uncertainty from measured parameter-value pairs.
Read how Experimentation for Engineers explains squared exponential kernel →
Ensemble Methods for Machine Learning
An exponential smoothing kernel assigns similarity weights that decrease exponentially with the squared distance between two inputs.
- How it is used
- Weights perturbed samples so LIME can fit a locally focused explanation around one black-box prediction.
- How deep it goes
- Defines the equation, distance weighting, and width parameter, then applies the kernel to local surrogate fitting.
- Examples
- Uses perturbed five-feature examples and a visual LIME neighborhood whose closer samples receive larger weights.
- What you can do after
- Apply it via LIME to emphasize local samples when explaining XGBoost predictions.
Read how Ensemble Methods for Machine Learning explains squared exponential kernel →
Related concepts
- radial basis function kernelequivalent to · A radial basis function kernel is a similarity function whose value depends on the distance between inputs and typically decreases as that distance increases.
- kernel functionkind of · A kernel function is a mathematical function that measures similarity between pairs of inputs, often representing an inner product in an implicit feature space.
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