# Why are (“non-parametric”) Gaussian Processes a good fit for Bayesian Optimization

I understand why Gaussian Processes are considered "non-parametric", but why do most authors use non-parametric models for Bayesian Optimization?

What's the benefit of using such models as opposed to parametric approaches? (GLM, etc.)

## 2 Answers

Parametric models assume the samples are from a specific distribution e.g. from a mixture of Gaussians where the number of Gaussian components is known a priori. This is restrictive since for most real-word problems we cannot know beforehand how complex the data is. For example, a nonparametric method should find the number of Gaussian components itself. As you see in my example, the nonparametric method still assumes something, that the data is from a mixture of Gaussians. But does not assume the number of components. Gaussian processes are nonparametric too. It uses every single training point to build a basis. So GP methods are flexible and powerful. They can learn complicated distributions (or decision boundaries in case of Gaussian process classification).

There's no any evidence why objective function should be linear, so nonparametrics like gaussian processes, random forests or neural networks are used as surrogates to approximate it as nonlinear function.

• you may say, let's use parametric models like n-degree polynomials or splines, but Gaussian Processes can be considered as generalization of them – Sengiley Jan 6 '17 at 20:24
• Yes but could not one argue that there is no evidence, either, that an objective function would fit any other model? I.e. all models are equally likely to be a good fit in the absence of data, unless you know something about the objective function? – Josh Jan 9 '17 at 19:28