About Volume Sampling.

[huaiguang233]

Hi,

Impressive work, I read your papers from BADGE to Gone Fishing and this one.
Volume sampling seems to be a very niche area, kind of like the determinantal point process, and I have two questions about this part:

1. I noticed in your paper that "A typical way of doing volume sampling is to select a batch of points with probability proportional to the determinant of their gram or covariance matrix" In the reference given (Kulesza et al., 2012), I didn't find an explanation of this part, if it is convenient, can you give me the source of this statement?
2. for the formula pt ∝ det (ˆΣt + g(xt)g(xt)⊤), what is the rationale behind adding the covariance matrices directly, I don't quite understand the rationale behind this formula.

thanks,
Hua