Loss with NLL of mark and MAE of inter-event time about ifl-tpp HOT 4 CLOSED

Yes, this is fine if you only care about MAE/MSE + accuracy. You could simply use the context tensor to obtain the (point estimate of the) next inter-event time and train using the objective function that you specified. The code will look something like

features = self.get_features(batch)
context = self.get_context(features)
m = F.softplus(self.linear_time(context))
mae = torch.abs(m - batch.inter_times).sum(-1)

Then you could train this model using the objective function that you wrote above (I assume the absolute value is missing in the first term after =).

You can interpret this as a TPP model where the conditional distribution over the inter-event times has density p(tau) ∝ exp(-|tau - m|). Note that this is not the Laplace distribution with mean m: Laplace distribution is supported on (-\infty, \infty), but this inter-event time distribution is supported on [0, infty). This distribution doesn't have a name, I don't know how to compute its density and I it's probably impossible to sample from it. However, if you only care about MAE/MSE + accuracy, this shouldn't be a problem. What we have here is rather a truncated Laplace distribution.

If, however, you compute MAE as mae = (torch.abs(m - batch.inter_times) / batch.inter_times).sum(-1), then I'm quite sure that this doesn't have an interpretation as a conditional density. You can still train your model with this loss just like before though, if you don't care about other things like sampling.

from ifl-tpp.

Thank you for your reply! It helped me a lot.

Why exactly p(tau) ∝ exp(-|tau - m|)? Can I interpret this also as an TPP with p(tau) ∝ exp(-(tau - m)^2). So to say, a "Gaussian" distribution on [0, infinity)?

from ifl-tpp.

Yes, your statement about p(tau) ∝ exp(-(tau - m)^2) is correct. Btw, here is a Wikipedia page about such truncated distributions https://en.wikipedia.org/wiki/Truncated_distribution.

I will also provide some context here. A TPP is a generative model for variable-length continuous-time event sequences. We usually train such models by maximizing the log-likelihood of the training sequences. You can interpret some losses, such as MAE or MSE, as the negative log-likelihood of some TPP model where the conditional distribution p*(tau) over the inter-event times has a special form. However, it doesn't mean that only losses that have this interpretation are "valid". In fact, if you only care about a point estimate of the next inter-event times (as measured by MAE/MSE) or of the accuracy of mark prediction, you don't even need a TPP model–you can directly optimize the loss that you care about. You should only worry about the "probabilistic" interpretation if you want to draw samples from the trained generative model.

Put differently, I don't quite understand why MAE/MSE is used to evaluate TPPs. TPPs proposed in the literature usually define the entire distribution over the inter-event times, but MAE/MSE only care about a point estimate. I can totally imagine cases where MAE/MSE are useful metrics, but I don't think we should use TPPs in such scenarios–a simpler model that only produces a point estimate instead of the entire distribution will probably do much better.

from ifl-tpp.

Thank you for the link to the Wikipedia page.

Yes, I agree with you that if one just need the point estimate, a TPP is not necessary. For my application I tried both approaches for computing the point estimate - with and without TPP. Calculating the point estimate from the context vector without TPP worked better.

from ifl-tpp.