Gaussian process
A Gaussian process is a probability distribution over functions in which every finite collection of function values has a joint Gaussian distribution.
Bayesian Optimization in Action
A Gaussian process is a probabilistic model over functions that defines predictive distributions, including means and uncertainties, at unobserved inputs.
- How it is used
- Models expensive black-box objectives as BayesOpt surrogate models that inform which input to evaluate next.
- How deep it goes
- Defines GPs through finite multivariate-normal subsets, explains prior-to-posterior behavior, and implements exact models; later scaling issues are identified.
- Examples
- Uses housing-price regions, prior and posterior function plots, and one-dimensional black-box optimization iterations.
- What you can do after
- Build exact GPyTorch GP models, visualize predictive distributions, train them with gradient descent, and use them within BayesOpt.
Read how Bayesian Optimization in Action explains Gaussian process →
AI-Powered Search
A Gaussian process is a collection of random variables whose finite subsets have joint Gaussian distributions and that defines a probability distribution over functions.
- How it is used
- Balances exploitation of known ranking behavior with exploration of underobserved query–document combinations.
- How deep it goes
- Explains probabilistic prediction, uncertainty, expected improvement, and implementation, but stops short of deriving Gaussian-process mathematics.
- Examples
- Uses river-depth observations, feature combinations, and the “transformers dvd” product-selection example.
- What you can do after
- Apply it via scikit-learn to rank search candidates by expected improvement and select products for exploration.
Machine Learning Algorithms in Depth
A Gaussian process is a collection of random variables such that every finite subset has a jointly Gaussian distribution, defining a probability distribution over functions.
- How it is used
- Models a distribution over functions for continuous-value regression and for performance functions in Bayesian optimization.
- How deep it goes
- Derives noiseless regression predictions by Gaussian conditioning and implements a radial basis function example from scratch.
- Examples
- Uses CO₂ prediction, prior-versus-posterior samples, and hyperparameter searches for support vector machines and random forests.
- What you can do after
- Build it from scratch to compute regression posterior predictions, then evaluate/understand its role in Bayesian optimization.
Read how Machine Learning Algorithms in Depth explains Gaussian process →
Related concepts
- language modelkind of · A language model is a computational model that represents patterns in linguistic tokens to estimate sequence probabilities and predict or generate language from context.
- mean functionhas part · A mean function maps an input to the expected value of a random function before conditioning on observed data.
- covariance functionhas part · A covariance function, also called a kernel, specifies the covariance between function values at pairs of inputs in a Gaussian process.
- Bayesian optimizationused by · Bayesian optimization is a sequential method for optimizing an expensive or unknown objective by using a probabilistic model to guide evaluations.
- kernel functionuses · A kernel function is a mathematical function that measures similarity between pairs of inputs, often representing an inner product in an implicit feature space.
- radial basis function kerneluses · A radial basis function kernel is a similarity function whose value depends on the distance between inputs and typically decreases as that distance increases.
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