Derivative of histc not implemented

1

I am trying to make a density estimation of a sample of data to compute a divergence between probability distributions. I used torch.histc to histogram my data so I could very roughly approximate the pdf. However, upon backpropagating I receive the error:

“the derivative for “histc” is not implemented”

Does anyone know how to work around this so I could bin my data and normalize it to make this calculation differentiable?

2

The histc function did not implemented backward operation is because it is a discrete operation (I really don’t know how would you define that exactly). But the value could be added to some other loss. I tested with the following code.

Noted: the loss will be updated respect to lossB below. And I am not sure how would you applied that to your problem

The setup

class TestModule(nn.Module):
    def __init__(self):
        super(TestModule, self).__init__()
        self.sigmoid = nn.Sigmoid()
        self.conv = nn.Conv2d(1, 1, 3, padding=1)
        
    def forward(self, x):
        x = self.conv(x)
        x = self.sigmoid(x)
        return x

model = TestModule()
optimizer = optim.Adam(model.parameters())

isAborted = True
def loop_stack(loss, acc):
    global isAborted
    if isAborted:
        return
    if loss == None:
        print(list(reversed(list(map(lambda x: str(x)[1:-1].split(" ")[0], acc)))))
        return
    new_acc = acc[:] + [loss]
    try:
        losses_child = list(map(lambda x: x[0], loss.next_functions))
        for l in losses_child:
            loop_stack(l, new_acc)
            if isAborted:
                break
    except KeyboardInterrupt:
        isAborted = True
        return
    except:
        print(list(reversed(list(map(lambda x: str(x)[1:-1].split(" ")[0], acc)))))
        return
    
def print_backprop(loss):
    global isAborted
    tmp = loss.grad_fn
    isAborted = False
    loop_stack(tmp, [])

The execution:

source = torch.rand(1, 1, 5, 5)
target = model(source)
s = source.contiguous().view(-1)
t = target.contiguous().view(-1)

t_min = torch.min(torch.cat((s, t), 0)).item()
t_max = torch.max(torch.cat((s, t), 0)).item()
n_bins = 4

s_his = torch.histc(source, bins=n_bins, min=t_min, max=t_max)
t_his = torch.histc(target, bins=n_bins, min=t_min, max=t_max)

lossA = F.mse_loss(s_his.detach(), t_his.detach())
lossB = F.mse_loss(source, target)

optimizer.zero_grad()
loss = lossB/lossB.detach()*lossA #(lossB/lossB)*lossA

loss.backward(retain_graph=True)
optimizer.step()

print("Loss: {}\tBack prop path".format(loss))
print_backprop(loss)
print()

print("Before:\n{}\n\n{}\n=============".format(source, target))
print("After:\n{}\n\n{}".format(source, model(source)))

The final result showed that the weight is updated (somehow).

There are a few things I still don’t know
like is the weight updated with lossB with magnitude of 1 or with magnitude of loss calculated with lossA

If I missed anything please reply or message me (I’m really curious)

3

It’s hard to define the derivation of histogram due to its potential constrains (sum(hist)=1 or sum(hist) = N). The weightsof histogram vector are not independent. Increase of one bin will certainly cause decrease of other bins.