# Gaussian mixture vs. Gaussian process

As far as I know, both Gaussian mixtures as well as Gaussian processes can be used for regression. My question is: what is better and why?

The answers might contain theoretic insights, practical experience or reference to further resources.

EDIT

I would like to know which one is better for approximation of nonlinear regression problems $$Y_i=g(x_i)+V_i$$ where $V_i\sim\mathcal{N}(0,\sigma^2)$ for all considered $i$. The function $g(\cdot)$ is assumed to be continuous. For the simplicity sake, we can admit that $x_i\in\mathbb{R}$. The criterion is the one-leave out mean square error.

The second criterion, perhaps more important. Since I assume that both (GM and GP) have the universal approaximation property, I would be curious which one is less complex (in terms of time and/or memory) in order to obtain given level of error.

Finally, I assume that the new data points $(x_i,y_i)$ can be generated on demand with a constant computational compexity.

• "Better" for what purpose and context? You might as well ask "which is better--digging with a spade or digging with a fork--and why?" Please, then, edit this question to provide this information that is essential for getting objective, useful answers. – whuber Oct 21 '14 at 18:12

To answer your last question, Gaussian process is a discriminative model as opposed to generative. Therefore, you will not be able to model $p(x, y)$ using Gaussian process. Gaussian process models $p(y | x)$ instead. To generate samples $(x_i, y_i)$ you need to work with a generative model such as Gaussian mixture model.