GMM explainations

[josiahls]

Sorry if this is a little open ended. I am making a pytorch dads implementation and have never worked with GMMs before. I am curious about the behavior I should expect from a GMM. Currently I have a toy problem just to show what kind of data I'm playing with:

hot_air_ballon_start_states=torch.rand((5,1))
hot_air_ballon_start_actions=torch.rand((5,1))-0.5
hot_air_ballon_next_states=hot_air_ballon_start_states+hot_air_ballon_start_actions

next_timesteps=hot_air_ballon_next_states-hot_air_ballon_start_states    
x=torch.hstack([hot_air_ballon_start_states,hot_air_ballon_start_actions])
dist=gmm(x)

Full example and code: here
Note: I do plan to use batch norm and feed in a fully connected layer into the GMM like in the DADS implementation but I trying to get an mvp right now.

From my understanding, the GMM can:

• Be used to predict what the next state will literally look like.
• Used to predict the current probability of the next state given the input.
  So basically, GMMs can do double-duty of generating and evaluating data which is cool.

Some questions:

• Can GMMs overfit? For debugging purposes I am wondering whether I should expect my GMM to be exact or whether I can only hope that it gets somewhere close. For example below:
  

• Is there any guide on how many components I should use for a GMM? At what point should the number of components increase? Is this mostly trial and error?

• When should you fix_variance?

• Is use_modal_mean only possible when the number of components > 1?

  • Does a GMM perform worse if components > 1 and use_modal_mean==False?

• How do GMMs scale? If I flatten an image, does this become intractable?

Also let me know if there is a better forum to ask you all about this :)