Chengcheng-Guo
commented
1 year ago Hi, we really appreciate that.
The objective functions for Graph Cut is $f(X, V) = \lambda\sum{v \in V} \sum{x \in X} s(x, v) - \sum{x, y \in X} s(x, y)$ and for Facility Location $f(X, V) = \sum\limits{v \in V} \max_{x \in X} s(x, v)$, where $X$ is the subset, $V$ the ground set, and $s$ a similarity function. Therefore, while maximizing them, we don't have to explicitly input gradients, but we simply input a similarity matrix among samples as it is done in DeepCore. As for why last-layer gradients instead of other sample information are used to construct the similarity matrix, we have taken reference from the paper Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds. It gives empirical analysis of using gradients to compute similarity.
HoodieSJ
Hi. i am really grateful for your github.
I have question about the detailed application about submodular functions. (i.e. facility location, Graph Cut). It seems like the inputs utilized for submodular selection is per-sample gradients in the training dataset.
How do we define the objective functions for submodular selection (when inputs are gradients)? In the paper "Submodular combinatorial information measures with applications in machine learning", it provides the detailed procedure, however, it is hard to understand how the gradient is utilized to composite the objective function.