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ARD Kernel
Automatic Relevance Determination kernel that assigns a distinct length scale to each input dimension, allowing the Gaussian process model to identify the most influential variables.
Spectral Mixture Kernel
Non-stationary kernel constructed as a weighted sum of stationary base kernels with distinct parameters, enabling the capture of multi-scale structures and local variations in the objective function.
Variable Length Scale Kernel
Kernel where the length scale parameters are themselves functions of the input, conferring the underlying Gaussian process with a non-stationarity property to adapt to changing local dynamics.
Additive Covariance Structure Kernel
Kernel that decomposes the objective function into a sum of functions from subsets of input dimensions, leveraging the additive structure to enhance optimization efficiency in high dimensions.
Deep Gaussian Process Kernel
Implicit kernel resulting from the composition of multiple Gaussian processes, where the output of one layer serves as input to the next, enabling the modeling of complex hierarchical and non-linear structures.
Warping Kernel
Kernel that applies a non-linear transformation (warping) to the inputs or outputs of a base kernel, allowing the modeling of objective functions with complex anisotropies or non-stationarities.
Orthogonal Basis Functions Kernel
Kernel constructed from a series expansion of orthogonal functions (e.g., Legendre polynomials, trigonometric functions), offering increased interpretability and better extrapolation in certain contexts.
Gibbs Kernel
Non-stationary kernel where the covariance function depends on the position in the input space, defined via a local variance function and a local length scale function.
Bochner Kernel
Stationary kernel whose form is determined by its spectral density via Bochner's theorem, providing a theoretical framework for designing kernels with specific frequency properties.
Graph Kernel
Kernel defined on structured graph data, measuring similarity between two graphs by counting common substructures (e.g., paths, trees, cycles), used for optimization on discrete spaces.
Multiple Kernel Gaussian Process Regression
Approach where the final kernel is a linear or non-linear combination of multiple base kernels, automatically learned from data to capture different components of the objective function.
Local Stationarity Kernel
Kernel that models the objective function as locally stationary in neighborhoods of the input space, with slowly varying covariance parameters, offering a compromise between flexibility and interpretability.
Singular Value Decomposition Covariance Kernel
Kernel constructed by performing singular value decomposition (SVD) on an initial covariance matrix, allowing noise reduction and capturing the main directions of variation of the objective function.
Heteroscedasticity Kernel
Kernel that models input-dependent noise variance, essential for Bayesian optimization when the precision of objective function observations varies spatially.
Kronecker Covariance Structure Kernel
Kernel that exploits the Kronecker product structure in the covariance matrix, typical for objective functions on grids or tensors, reducing computational complexity from O(N^3) to O(N).
Convex Kernel Regression
Kernel designed to impose a convexity (or concavity) constraint on the Gaussian process model, used for optimization of functions known to be convex to improve convergence.