# Mixture Density Network: determine the parameters of each Gaussian component

This is a good paper, but I am still confused about a few small details. I am wondering if anyone could give me some help:

1. Basically the mixing coefficient alpha_i can be computed through a softmax function in eq (25) below. However, in eq (25), what's the upper alpha for each $(z_i)^{alpha}$? Is it a free parameter to be fitted?

2. Similarly, in eq (26), what's the upper sigma in $(z_i)^{sigma}$? Is it a free parameter to be fitted as well? Thanks!

• I edited the equations due to unreadability, please check them. – Media Aug 6 '18 at 21:37

• In your example, Does this mean that $(a_k)^{pi}$, $(a_{kl})^{mu}$, $(a_k)^{sigma}$ are just 3 different output variables? So does in my example, $(z_i)^{alpha}$ and $(z_i)^{sigma}$ are just two different output variables (one corresponds to the mixture coefficient, and the other one corresponds to sigma). The alpha and sigma are just variable index, am I understanding this correctly? – Edamame Aug 6 '18 at 23:16