I have a large set of simulation data that was generated using a Monte Carlo procedure that samples a distribution parameterized by (h, t). I want to use an InfoGAN model to provide unsupervised predictions classifications c of the simulation samples.

Now, it would be easy enough to just use the standard InfoGAN structure to do the unsupervised classification without using the external parameters (h, t), but I want the neural network to learn how c depends on (h, t). I would think that simply providing (h, t) as additional inputs to the generator and the discriminator will not provide the best results considering that for some parameters h_i and t_j that c_k is not guaranteed to exist. So, I cannot just independently sample h, t, and c when providing input for the generator. Instead, I would like InfoGAN to learn and optimize the I(c(h, t); G(z, c(h, t))) instead of I(c; G(z, c)) where c(h, t) is not known a priori.

In short, I suppose I am looking for a way to combine the unsupervised classification of InfoGAN while also providing additional conditional information as with CGAN in a way such that the relationship between the classification and the conditional information is learned.