# How to “use” Yolo Loss Function

I am dealing with Yolo Loss Function (the following). \begin{align} &\lambda_{coord} \sum_{i=0}^{S^2}\sum_{j=0}^B \mathbb{1}_{ij}^{obj}[(x_i-\hat{x}_i)^2 + (y_i-\hat{y}_i)^2 ] \\&+ \lambda_{coord} \sum_{i=0}^{S^2}\sum_{j=0}^B \mathbb{1}_{ij}^{obj}[(\sqrt{w_i}-\sqrt{\hat{w}_i})^2 +(\sqrt{h_i}-\sqrt{\hat{h}_i})^2 ]\\ &+ \sum_{i=0}^{S^2}\sum_{j=0}^B \mathbb{1}_{ij}^{obj}(C_i - \hat{C}_i)^2 + \lambda_{noobj}\sum_{i=0}^{S^2}\sum_{j=0}^B \mathbb{1}_{ij}^{noobj}(C_i - \hat{C}_i)^2 \\ &+ \sum_{i=0}^{S^2} \mathbb{1}_{i}^{obj}\sum_{c \in classes}(p_i(c) - \hat{p}_i(c))^2 \\ \end{align}

I cannot understand how to use it. That is, the "hat" variables are the right ones (related to the training set), while the standard variables are the predicted ones. However, it has some sense if there is a one-to-one corrispondence between the two kind of variables.

But what should happens if my model predicts an airplane while there are not?

I know the predicted center ($$x_i,y_i$$) and the predicted whidth and height ($$w_i,h_i$$) but since there are no airplanes what sould be the related hat variables?

Also, what is the meaning of $$\hat{p}_i(c)$$ since I have the certainess that that object belong to that class? It should be 1?