ROC Curve: Background Rejection vs. Signal Efficiency

[DannyJ108]

Hello forum,

I am reading this article on quantum machine learning. At one point in the article (page 7) they plot the ROC curve as background rejection vs. signal efficiency. Researching these concepts (since I did not understand them fully), I read that ROC curves should be plotted as TPR (True Positive Rate) vs. FPR (False Positive Rate). Also (I think), TPR can be called signal efficiency; and FPR can be called background rejection.

Why did they plot the ROC in the article I mentioned the way they did, contrary to what I've reasearched, which is always TPR vs. FPR? Any reason at all? Or is it just incorrect?

Thank you in advance!

 

[eljose79]

Hello,

Thank you for bringing up this interesting question. As a scientist in the field of quantum machine learning, I can provide some insights on why the authors may have chosen to plot the ROC curve as background rejection vs. signal efficiency.

Firstly, it is important to note that there are different conventions for plotting ROC curves. While it is common to plot TPR vs. FPR, some researchers may choose to plot background rejection vs. signal efficiency for various reasons.

One possible reason is that the authors may have wanted to emphasize the performance of their algorithm in terms of background rejection, which is a measure of how well the algorithm can distinguish between the signal and background data. By plotting background rejection on the y-axis, they may have wanted to showcase the high level of background rejection achieved by their algorithm.

Furthermore, in some cases, the signal efficiency may be a more important measure for the specific application being studied. For example, in medical diagnostics, it may be more critical to have a high signal efficiency (i.e. correctly identifying positive cases) rather than a low false positive rate. In such cases, plotting signal efficiency on the x-axis may provide a better visualization of the algorithm's performance.

It is also worth noting that TPR and signal efficiency are not exactly the same, although they are closely related. TPR is the ratio of correctly identified positive cases to the total number of positive cases, while signal efficiency is the ratio of correctly identified positive cases to the total number of cases (both positive and negative). Therefore, it is possible that the authors may have chosen to plot signal efficiency instead of TPR to provide a more comprehensive view of the algorithm's performance.

In conclusion, while TPR vs. FPR is the more commonly used convention for plotting ROC curves, there can be valid reasons for choosing to plot background rejection vs. signal efficiency instead. It is important to consider the specific context and goals of the study when interpreting the choice of axes in a ROC curve.

I hope this helps clarify the issue. If you have any further questions, please feel free to ask. Happy learning!