Is there any meaning to measure ture negative over all negative response? - machine-learning

When we want to assess the quality of a positive prediction made by the model, which is the number of true positives divided by the total number of positive predictions.
Also, the recall shows the model's ability to detect positive samples and biases towrds negative predictions, which is the ratio between the numbers of true positivto the total number of positive samples.
Is there any meaning in the ratio between True negative and all negative predictions??

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Selecting an IoU and confidence threshold for evaluation of model performance

mAP is commonly used to evaluate the performance of object detection models. However, there are two variables that need to be set when calculating mAP:
confidence threshold
IoU threshold
Just to clarify, confidence threshold is the minimum score that the model will consider the prediction to be a true prediction (otherwise it will ignore this prediction entirely). IoU threshold is the minimum overlap between ground truth and prediction boxes for the prediction to be considered a true positive.
Setting both of these thresholds to be low would result in a greater mAP. However, the low thresholds would most likely be inconsistent with the mAP scores from other studies. How does one select, and justify, these threshold values?
In Yolov5, we do NMS on the outputs of network, then calculate mAP. So, there is a conf_thres and an iou_thres in NMS to filter some boxes, these are set to 0.001 and 0.6, see: https://github.com/ultralytics/yolov5/blob/2373d5470e386a0c63c6ab77fbee6d699665e27b/val.py#L103.
When calculating mAP, we set iou threshold to 0.5 for mAP#0.5, or 0.5 to 0.95 with step 0.05 for mAP#0.5:0.95.
I guess the way of calculating mAP in Yolov5 is aligned to other framework. If I'm wrong, please correct me.

Why don't the false positive rate and true positive rate add up to one in a roc-auc curve?

The false positive rate is the x-axis spanning from 0 to 1. The true positive rate is the y-axis spanning from 0 to 1. And the graphs show data points like (.8,.8). Which if the tpr is .8 and the fpr is .8, they add up to 1.6...
Typically the axis are normalised using the total number of FPs or TPs in the test/validation set. Otherwise the end of the curve wouldn't be 1/1. I personally prefer to label the axis by the number of instances.
Why to not normalise by the total number - in real applications, it gets rather complicated as you often do not have labels for all examples. The typical example for ROC curves are mass mailings. To normalise the curve correctly you would need to spam the entire world.

ROC-Curve calculation of elements

I know that the ROC-Curve is calculated from the True-Positive-Rate and the False-Positive-Rate.
But the ROC-Curve has infinite Elements on it's Curve, right? How is each Element calculated? Can someone explain this to me? Where is each point coming from?
Example
Thanks in Advance
The values are calculated for all values of the threshold of the classifier.
On the x axis, you have the "false positive rate" for the given threshold: FPR = FP / (TN + FP) where:
FP are the number of false positive (the elements predicted positive but which are negative);
TN the number of true negative (the elements predicted negative and are really negative);
and FP the number of false positive (the elements predicted positive but are negative).
On the y axis, you have the "true positive rate" for the given threshold: TPR = TP / (TP + FN) where:
TP are the number of true positive (predicted positive and are indeed positive);
FN the number of false negative (predicted negative but are positive).
You have not an infinite number of points in practice: you are limited to the number of points of the dataset (the rate dont change for some ranges of threshold).

precision recall for depth estimation

I used Make3D dataset to estimate depth maps. I want to calculate precision and recall for each test image. But i have no idea how to do it with images specially how to find True/false positive and false negative from my results and the data.
I know only that :
Precision = tp/(tp+fp)
Recall = tp/(tp+fn)
With tp=True Positives, fp=False Positives and fn=False Negatives.
So how to calculate tp,fp and fn when i have pixels ?

Why represent neural network quality as 1 minus the ratio of the mean absolute error in prediction to the range of the predicted values?

The documentation for IBM's SPSS Modeler defines neural network quality as:
For a continuous target, this 1 minus the ratio of the mean absolute error in prediction (the average of the absolute values of the predicted values minus the observed values) to the range of predicted values (the maximum predicted value minus the minimum predicted value).
Is this calculation standard?
I'm having trouble understanding how quality is derived from this.
The main point here is to make the network quality measure independent from the range of output values. The proposed measure is 1 - relative_error This means that for a perfect network, you will get the maximum quality of 1. It also means that the quality cannot become less than 0.
Example:
If you want to predict values in the range 0 to 1, an absolute error of 0.2 would mean 20%. When predicting values in the range 0 to 100, you could have a much larger absolute error of 20 for the same accuracy of 20%.
When using the formula you describe, you get these relative errors:
1 - 0.2 / (1 - 0) = 0.8
1 - 20 / (100 - 0) = 0.8

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