Question About balanced Loss

[eric-tc]

Hi,

thanks for sharing the code and for your great work. I have a question about the loss in your paper why you add +1 in (1) formula exactly (1-p)(En-1+1). Where does it came from? is the initial expected value?

Thanks

[richardaecn]

Hi @eric-tc ,

In Figure 2, the volume of gray shaded region is E_{n-1}. After we sampled a new data, there are 2 possibilities showed in the right side of Figure 2:

1. with probability p = E_{n-1}/N, the newly sampled data is inside the gray region, so the new volume is unchanged (E_{n-1});
2. with probability 1-p, the newly sampled data is outside the gray region, so the new volume is added by 1 (E_{n-1} + 1);

Therefore, the expected new volume is Equation 1.

[eric-tc]

Hi @richardaecn ,
thanks now it is clear.