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Mixture density networks

It is a neural network whose output is a mixture of Gaussians.

$$p(y|x) = \sum_{i=1}^n p(c=i|x)N(y_i; \mu^{(i)}, \Sigma^{(i)(x)})$$

• $p(c=i|x)$ is the mixture prior, obtainable using softmax

• $\mu^{(i)}$ is the center of the ith component, if y is d dimensional an NN must produce a $n$ d dimensional vectors.

• $\Sigma^{(i)(x)}$ it is the covariance matrix in general it is chosen to be diagonal

Multivariate Gaussian Stochastic Encoder and Decoders