In active learning with estimators like Gaussian Processes, we typically look at the test-test covariance matrix, and choose for the next round of observation, the points who have the largest variance on the diagonal.
This comes from the intuition that observing these points would reduce the maximum amount of uncertainty, as measured by the variance.
However if we look at the off diagonal terms, an entire row, it keeps the covariance or relatedness of other samples with this one. So, observing a point that is highly covariant with others will not only reduce uncertainty about its own value ( just like the method above) but also have an impact on our uncertainty about the remaining unseen observations.
So, this suggests not just the diagonal terms but the sum of rows as the quantity from which we should pick the next points to observe (the ones with the highest row sum)
I'd like to know if this argument is correct, or i am missing something thanks.