No this does not make sense. You do not want a high FPR'. This is because it is impossible to have a generally high FPR' since the integral of FPR' from 0 to 1 is FPR(t) which has a change of exactly one. The concept of a generally higher FPR'(t) does not make sense. The other bit about the high TPR(t) is fine. But the FPR' part does not track. In addition, relating the FPR' for the two models AUC seemed to just blatantly be wrong? It is possible for two models with exactly the same FPR(t) to have different AUC values if their TPR(t) are different. So the differential equation described cannot be true. Perhaps I am missing something, but this explanation of AUC seems to get the calculus wrong. I am dubious of any conclusions drawn from it.
Hello, I simplified the integral further and found the result delta R^2, which shows that the value of the integral is not dependent on the curve, what is the implication of this?
for example any time you want to compute an expected value (which mathematically is an integral), but which doesn‘t have a convenient, practical or feasible solution. You can then instead sample the term in the expected value with the probability distribution of the random variable and thus use theMonte Carlo method to approximate the integral reformulated as an expectation.
May I ask what make you think so? We work with it in medical applications too, but the only downside I noticed, is that ROC-AUC is not a good metrics for cross-validation for training classificators on imbalanced data sets, because in this case ROC-AUC gives overly optimistic estimation on training data. Except this AUC looks fine..
No this does not make sense. You do not want a high FPR'. This is because it is impossible to have a generally high FPR' since the integral of FPR' from 0 to 1 is FPR(t) which has a change of exactly one. The concept of a generally higher FPR'(t) does not make sense.
The other bit about the high TPR(t) is fine. But the FPR' part does not track.
In addition, relating the FPR' for the two models AUC seemed to just blatantly be wrong? It is possible for two models with exactly the same FPR(t) to have different AUC values if their TPR(t) are different. So the differential equation described cannot be true.
Perhaps I am missing something, but this explanation of AUC seems to get the calculus wrong. I am dubious of any conclusions drawn from it.
I am wondering about binary classification when there are multiple variables/parameters.
TPR and FPR are Independent from the variables. Its a Metric calculated as Probability from the Output.
Hello, I simplified the integral further and found the result delta R^2, which shows that the value of the integral is not dependent on the curve, what is the implication of this?
However most of the integration in ML can only estimate by sampling
Can you give an example where integration is needed in the ML context where sampling is needed? I'd like to check that out and learn abou it 💪
for example any time you want to compute an expected value (which mathematically is an integral), but which doesn‘t have a convenient, practical or feasible solution. You can then instead sample the term in the expected value with the probability distribution of the random variable and thus use theMonte Carlo method to approximate the integral reformulated as an expectation.
a more specific example to look at is the variational autoencoder
It is marginal likelihood mostly if u want to study that kind of topics u can start with Gibbs sampling or Gaussian Processing
I would argue that the integral of the normal distribution is more fundamental for ds..
I'm sure ROCs have their uses, but I think their usefulness in medicine is usually overrated.
May I ask what make you think so? We work with it in medical applications too, but the only downside I noticed, is that ROC-AUC is not a good metrics for cross-validation for training classificators on imbalanced data sets, because in this case ROC-AUC gives overly optimistic estimation on training data. Except this AUC looks fine..
Great work..............................easy way of teaching......