GaußprozessAnsätzen

GaußprozessAnsätzen, often translated as Gaussian Process Approaches, refers to a family of machine learning methods that utilize Gaussian processes to model probability distributions over functions. Instead of directly learning a single function, Gaussian processes define a prior distribution over possible functions. This prior is then updated based on observed data to yield a posterior distribution that represents the learned function.

The core of a Gaussian process is its covariance function, also known as the kernel. The kernel defines the smoothness and similarity between function values at different input points. Common kernels include the radial basis function (RBF) kernel, which assumes smooth functions, and the Matern kernel, which allows for more flexible smoothness. By choosing an appropriate kernel, one can encode prior beliefs about the underlying function's properties.

When performing regression, a Gaussian process provides not only a mean prediction for unseen data points but also a measure of uncertainty in the form of variance. This uncertainty quantification is a significant advantage of Gaussian process approaches, making them suitable for tasks where understanding prediction reliability is crucial. For classification, Gaussian processes can be extended to model probabilities of class membership.

Gaussian process approaches are non-parametric, meaning their complexity grows with the amount of data. While powerful, they can be computationally expensive for large datasets due to the need to invert a covariance matrix whose size is proportional to the number of training points. Various approximation techniques have been developed to address this scalability challenge. They find applications in areas such as geostatistics, robotics, Bayesian optimization, and time series analysis.