LogQ in criterion.py

[nviwch]

def logQ(self, gt_uv, pred_jts, sigma):
return torch.log(sigma / self.amp) + torch.abs(gt_uv - pred_jts) / (math.sqrt(2) * sigma + 1e-9)

from the function definition, it looks like the Q is laplacian distribution but Q = exp( - abs(x - mu) / b) / 2b, after taking log it is log(1/2b) - abs(x - mu) / b

when seeing loss = nf_loss + Q_logprob, nf_loss = log(sigma) - log_phi, compare with the paper saying loss = -log(Q(bar_mu)) +log(sigma)-log_phi, I guess the Q_logprob already has the negative sign inside but then, why it is not -log(1/2b) + abs(x-mu)/b? i.e. the first term torch.log(sigma / self.amp) should have the minus sign.

On the other hand, how do you choose the value of b? in the distribution sense, b = sqrt(variance / 2)

[Jeff-sjtu]

Hi @nviwch ,

The first term - log(1/2b) = log(2b) = log(sigma) + log(constant). Therefore, it is equivalent to torch.log(sigma). The constant term can be ignored when calculating loss.

For the second question, b = sqrt(varance * 2) = sqrt(2) * sigma in our implementation.

[nviwch]

i don't know how I miss the next simple step. Sorry for my stupid question

[sunyizeng]

As @nviwch pointed out b = sqrt(variance / 2) = sigma / sort(2)
But in the implementation, b = sqrt(varance * 2) = sigma * sqrt(2)
Is this a bug? @Jeff-sjtu