Hi,I had couple of questions regarding VAE / AE / GMM that i’m sure can benefit others, but i’m not sure of the answer. I did try to look for answers, however the source was too hard for me to understand or i wasn’t able to find any.

- If you learn a multivariate instances, what do you assume during the learning? that the variables are independent? what if in reality they are dependent ? one conditioned on the other? non iid
- If i have a VAE, how can i sample from it? what type of sampling, their differences - pytorch/ keras implementation of sampling can be useful.
- What exactly do you sample? (if you have multivariate vector for instance)
- How can you guarantee the dataset distribution when you do sample? what does it mean in multivariate case. (I assume you must have KL loss and in some problems also RE - reconstruction error)
- Is it possible to sample out-of-distribution?
- Why VAE is better, if at all from GMM in generating multivariate distributions?
- How will you go about learning a multivariate distribution of both continues and categorical variables? how will you evaluate them? VAE/ GMM / other?
- Gumbel softmax / The Straight-Through estimator/ other ? what are their pros / cons

Thank you! appreciate any answer, feel free to add / correct. I’m a new to AE and i feel the sources out there are or too mathematical but don’t answer the above, or too low level.

Thank you!