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No, you can't extract any probability from a fuzzy membership grade. The uncertainty expressed by fuzzy logic is about partial truth, not about probability. $ \mu_S(x) = 0.9 $ doesn't mean that "$ x $ is tall" is true with a probability of 0.9, but that "$ x $ is tall" is 90% true (notice the difference in semantics). You have to think ...


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Also, in general, in the conditional expectation, which distribution do we compute the expectation with respect to? From what I have seen, in $\mathbb{E}[X|Y]$, we always calculate the expected value over distribution $X$. No, for $\mathbb{E}[X|Y]$ we take expectation of $X$ with respect to the conditional distribution $X|Y$, i.e. $$\mathbb{E}[X|Y] = \...


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Bayes Error Rate For the general case of K different classes, the probability of classifing x instance correctly is: \begin{equation} \label{eq1} \begin{split} P(correct) & = \sum_{i=1}^{K} p(x \in H_i, C_i) \\ & = \sum_{i=1}^{K} \int_{x \in H_i} p(x,C_i) \, dx\\ & = \sum_{i=1}^{K} \int_{x \in H_i} P(C_i|x)p(x)\,dx \\ \end{split} \end{equation} ...


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Of course you can use AI (specially Deep Learning) in your application. your covariates will be the input to your AI model and the model should predict probability of presence. The model has no problem with binary data and binary data is common in this field. Also note that 1:100 ratio is not good and the network will probably learn to output absence for any ...


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Your call to model.predict() is returning the logits for softmax. This is useful for training purposes. To get probabilties, you need to apply softmax on the logits. import torch.nn.functional as F logits = model.predict() probabilities = F.softmax(logits, dim=-1) Now you can apply your threshold same as for the Keras model.


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Figure 3 in the original WGAN paper is actually quite helpful to understand the difference between the score in WGAN and the probability in GAN (see screenshot below). The blue distribution are real samples, and the green one are fake samples. The Vanilla GAN trained in this example identifies the real samples as '100% real' (red curve) and the fake samples ...


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