Gaussian Processes for Nonlinear Signal Processing

Gaussian processes (GPs) are Bayesian state-of-the-art tools for discriminative machine learning, i.e., regression [1], classification [2] and dimensionality reduction [3]. GPs were first proposed in statistics by Tony O'Hagan [4] and they are well-known to the geostatistics community as kriging. However, due to their high computational complexity they did not become widely applied tools in machine learning until the early XXI century [5]. GPs can be interpreted as a family of kernel methods with the additional advantage of providing a full conditional statistical description for the predicted variable, which can be primarily used to establish confidence intervals and to set hyper-parameters. In a nutshell, Gaussian processes assume that a Gaussian process prior governs the set of possible latent functions (which are unobserved), and the likelihood (of the latent function) and observations shape this prior to produce posterior probabilistic estimates.