Review of 3 papers from Kulesza and Taskar on DPP.
Determinantal Point Process: , where Y is a discrete set of points, and K is a kernel on Y.
The benefit of DPP is that its partition function can be computed in closed form, as well as marginals and conditionals. To sample from a DPP, we need to use the eigen-decomposition of K. It captures repulsion between points to enforce diversity.
The 3 papers of Taskar looks at a few variations on this theme:
- Structured DPP. K can be decomposed as , where we think of q as the (scalar) quality of a point and as a feature vector. The structure comes in where we can have and decompose and . Applied it to estimate pose (odd choice). Not sure the details.
- k-DPP. The regular DPP can generate subsets of points of various sizes. k-DPP basically constrains it to generate exactly k points. Applied to find sets of diverse images. The learning is over a convex sum of different kernels (i.e. learn the weights on a training set).
- Learning. Treat the quality , and optimize over from training set. Applied to text summarization.