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ALEBO (Adaptive Linear Embeddings for Bayesian Optimization)
Bayesian optimization technique that learns a low-dimensional linear subspace to project high-dimensional points, thereby reducing computational complexity.
ADD-GP (Additive Gaussian Process)
Additive Gaussian process model that decomposes the objective function into a sum of functions of variable subgroups, enabling better scalability in high dimensions.
Gaussian Process (GP)
Non-parametric probabilistic model defining a distribution over functions, widely used as a surrogate in Bayesian optimization to model uncertainty.
Acquisition Criterion
Heuristic function used in Bayesian optimization to guide the choice of the next evaluation point by balancing exploration and exploitation.
Expected Improvement (EI)
Popular acquisition criterion that calculates the expected improvement relative to the current best observation, weighted by the model's uncertainty.
Dimensionality Embedding
Dimensionality reduction technique that projects the high-dimensional search space into a lower-dimensional subspace where optimization is performed.
Additive Structure
Assumption that the objective function can be decomposed into a sum of functions depending on subsets of variables, exploited to improve efficiency in high dimensions.
High-Dimensional BO (Bayesian Optimization)
Variant of Bayesian optimization adapted to search spaces with tens or hundreds of dimensions, requiring specialized techniques.
Surrogate Model
Approximate model of the expensive objective function, used in Bayesian optimization to predict values and uncertainty at unevaluated points.
ARD Kernel (Automatic Relevance Determination)
Gaussian process kernel that automatically learns the importance of each dimension, enabling identification of relevant variables in high dimensions.
Random Embedding
Technique that randomly projects the high-dimensional space into a lower-dimensional subspace, assuming only a few directions are relevant.
Trust Region BO
Bayesian optimization method that restricts the search to a trust region around the current best solution, suitable for high-dimensional problems.
GP-UCB (Gaussian Process Upper Confidence Bound)
Acquisition criterion that balances exploration and exploitation using an upper confidence bound on the Gaussian process prediction.
Kernel Factorization
Approach that decomposes the Gaussian process kernel into a product of one-dimensional kernels, reducing computational complexity in high dimensions.
High-Dimensional Multi-Objective Optimization
Extension of Bayesian optimization to problems with multiple conflicting objectives in high dimensions, requiring adapted acquisition criteria.
Bayesian Optimization with High-Dimensional Outputs
Variant where the objective function returns high-dimensional vectors, requiring multi-output models and specialized acquisition criteria.