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Review by Dilshan Godaliyadda

This slecture is very well written with a significant amount of effort put in to it. The introduction sections is very well structured. Dennis starts by stating the intention of the slecture, and briefly describes how the document is structured. Then he provides a motivating example, which was particularly good, because it shows how important it is to incorporate Risk in Bayes Rule. Then he describes the theoretical framework of how to incorporate Risk into Bayes rule. He arrives at a cost function which is the Expected Risk, and finally states a classification rule that would minimize it. Then, he gives two clear examples for 1D and 2D feature classification. He concludes the slecture with an example, which allows the reader to see how the classification changes as risk is incorporated.

I do have a few minor suggestions that I believe could make this slecture even better:

• On the "Bayes rule for minimizing risk" Section:
  • The line that says 'We assign x so that cost is minimized:" is a bit unclear, consider replacing with something like "We assign x to class 1 or 2 according to:", since that will make an easier transition to Eq(2).
  • The following comments relate to the equation array containing Eq(3)
    • Lines 4,5: consider using parenthesis around integrand
    • Might be clearer if you state what R_1 and R_2 are soon after line 4
    • Before you arrive at line 5 you can state what is used to get to line 5 rather than after. This will mean that you will not be able to use equation array for the last line, but it will enable you to label the equation (Eq(3)) right next to the equation you are using afterward, which i believe could make it clearer for later referencing.
  • The last part of the theory where you talk about minimizing the cost in equation 3, it would be great if you can give a little bit more of an explanation.
  • Just to make things a bit more clear, you can also think about starting to talk about how to minimize the cost on a new line.
• On the "Example 1: 1D features" Section:
  • Where you say "an equivalent formulation" it would be great if you can start on a new line. Since otherwise it might seem like you are adding onto the statement already made in that paragraph.
• On the "Example 2: 2D features" Section:
  • Consider increasing the size of the plot, since that would make the crosses and circles easier to see.

Author's reply

Thank you Dilshan for your excellent comments. I've made the changes that you've recommended, and I hope that now I have addressed all of your comments. -Dennis

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