Kernel function
A kernel function is a mathematical function that measures similarity between pairs of inputs, often representing an inner product in an implicit feature space.
Grokking Machine Learning
A mathematical function that represents an inner product in a transformed feature space, allowing a model to learn nonlinear decision boundaries.
- How it is used
- Uses kernels with SVMs to classify datasets that lack a linear decision boundary.
- How deep it goes
- Explains similarity, feature mapping, and RBF and polynomial examples, while deferring the full theory of kernels and feature maps.
- Examples
- Uses XOR, circular and one-dimensional datasets to illustrate polynomial and RBF kernel classification.
- What you can do after
- Apply via SVC by selecting a polynomial or RBF kernel and setting its degree or gamma.
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Causal Inference for Data Science
A kernel is a weighting function that assigns observation weights according to distance from a target point.
- How it is used
- Weights nearby observations more heavily when estimating local effects in regression discontinuity designs.
- How deep it goes
- Defines two kernels, shows bandwidth transformation, and defers elaborate bandwidth selection to package documentation.
- Examples
- Uses uniform and triangular functions, kernel figures, and local estimation around a time cutoff.
- What you can do after
- Evaluate how kernel choice and bandwidth control which observations influence a local regression estimate.
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Experimentation for Engineers
A kernel function assigns a similarity or weight to an observation based on its distance from another input.
- How it is used
- Weights nearby measurements when Gaussian process regression estimates CPU time in Bayesian optimization.
- How deep it goes
- Defines distance-based weighting, implements squared exponential kernels and normalization, but defers leave-one-out cross-validation details.
- Examples
- Uses CPU-time measurements at parameters 0.5 and 0.0, evaluates queries 0.25 and 0.4, and plots surrogate curves.
- What you can do after
- Apply it via NumPy to normalize distance-based weights and estimate query values from measured parameters.
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Machine Learning Algorithms in Depth
A positive-definite function that measures similarity between pairs of inputs and defines an associated feature-space inner product.
- How it is used
- Supplies pairwise similarities in an SVM dual and covariance between function values in Gaussian process regression.
- How deep it goes
- Connects kernels to SVM dual optimization and GP posterior conditioning, then implements RBF evaluations without explicitly constructing feature vectors.
- Examples
- Uses RBF kernel code for an SVM and GP regression, alongside graph, string, and document kernels as other similarity measures.
- What you can do after
- Build it from scratch in an SVM optimized with CVXOPT or in Gaussian process regression using NumPy and SciPy.
Read how Machine Learning Algorithms in Depth explains kernel function →
Related concepts
- feature mapproduces · A feature map is a spatially organized array of neural-network activations representing the presence or strength of learned features at different locations.
- covariance functionequivalent to · A covariance function, also called a kernel, specifies the covariance between function values at pairs of inputs in a Gaussian process.
- kernel density estimateused by · A kernel density estimate is a nonparametric probability-density estimate formed by combining localized kernel functions centered on observed data points.
- similarity metrickind of · A similarity measure is a rule that quantifies or characterizes how alike two objects or representations are according to selected properties.
- radial basis function kernelincludes · A radial basis function kernel is a similarity function whose value depends on the distance between inputs and typically decreases as that distance increases.
- support vector machineused by · A support vector machine is a supervised-learning model that uses support vectors to determine a maximum-margin decision boundary or regression function, optionally using kernels to model nonlinear relationships.
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