Ah, a conditional VAE!
Small question: Am I the only one that reserves ‘z’ for the latent variables of the autoencoder? You seem to be using it as the ‘predictor state’ input. Or am I reading it wrong?
Now I understand your P(z|Q,A) better, as it’s just the conditional generator. But, how do you get P(A|Q)? That distribution need not be the same for the human known set and the total set.
I was wondering what happens in deployment when you meet a z that’s not in your P(z,Q,A) (ie very small p). Would you be sampling P(z|Q,A) forever?
You aren’t the only one, z is usually used for the latent, I just followed Paul’s notation to avoid confusion.
P(A|Q) comes just from training on the QA pairs. But I did say “set any reasonable prior over answers”, because I expect P(z|Q,A) to be orders of magnitude higher for the right answer. Like I said in another comment, an image generator (that isn’t terrible) is incredibly unlikely to generate a cat from the input “dog”, so even big changes to the prior probably won’t matter much. That being said, machine learning rests on the IID assumption, regular reporters are no exception, they also incorporate P(A|Q), it’s just that here it is explicit.
The whole point of VAEs is that the estimation of the probability of a sample is efficient (see section 2.1 here: https://arxiv.org/abs/1606.05908v1), so I don’t expect it to be a problem.
Ah, a conditional VAE! Small question: Am I the only one that reserves ‘z’ for the latent variables of the autoencoder? You seem to be using it as the ‘predictor state’ input. Or am I reading it wrong?
Now I understand your P(z|Q,A) better, as it’s just the conditional generator. But, how do you get P(A|Q)? That distribution need not be the same for the human known set and the total set.
I was wondering what happens in deployment when you meet a z that’s not in your P(z,Q,A) (ie very small p). Would you be sampling P(z|Q,A) forever?
You aren’t the only one, z is usually used for the latent, I just followed Paul’s notation to avoid confusion.
P(A|Q) comes just from training on the QA pairs. But I did say “set any reasonable prior over answers”, because I expect P(z|Q,A) to be orders of magnitude higher for the right answer. Like I said in another comment, an image generator (that isn’t terrible) is incredibly unlikely to generate a cat from the input “dog”, so even big changes to the prior probably won’t matter much. That being said, machine learning rests on the IID assumption, regular reporters are no exception, they also incorporate P(A|Q), it’s just that here it is explicit.
The whole point of VAEs is that the estimation of the probability of a sample is efficient (see section 2.1 here: https://arxiv.org/abs/1606.05908v1), so I don’t expect it to be a problem.