let’s say I have a data set with 100 features and a couple million of samples. Whenever I get a new sample, I would like to estimate how many samples would have been around it in the original set (let’s say within L1 distance of $varepsilon$). How can I do this in an efficient way? To me it sounds like I would like to estimate (joint) density function at a particular point. Perhaps, there’s a way to train a neural net that outputs such density function based on the features values.
Motivation: I would like to use this density function value at a particular point in order to understand how confident should I be in my prediction at that point (the higher the density, the higher would my confidence be).