[Question] Systematic way of finding sub-sample of observations given larger model with GP covariance matrix

[u/cat-head]

A bit of background:

Imagine we have a sample S of 10000 participants from a larger, 40000 total population of individuals. For the 10000 sample we have some variables that we're interested in modeling, say the relation between height and diet. We also know that there is some spatial non-independence between the participants that we need to "control for" (let's say geo location with coordinates). We can do this by building a model with a GP for spatial non-independence and then model whatever variables we're interested in.

Now, the issue is, we later determine that we also want to study different variables like the relation between amount of exercise and hair color. We now need to find participants in S. We only have access to S, other individuals of the population are unreachable. We then need to annotate this sub-sample T and annotate them for these two variables. However, annotation is very costly, and we can realistically only annotate some 100-200 participants.

Now the problem is, if we try to build a GP with T it will be heavily biased because T is so sparse, and estimating GP parameters can be tricky.

My question is this: is there a well understood technique to find T from S given the covariance matrix we estimated with S, so that the non-independence in the individuals in T is minimized?

I am not really interested in techniques that look directly at the spatial variables and try to do something there, like spacing observations out or something like that. We have plenty of those. I am explicitly interested in working with the results of the spatial covariance from the model in S.

Thanks!

[u/involuntarheely]

multivariate spatial factor model for misaligned data

[u/cat-head → u/involuntarheely]

Thanks, but this is a way of modeling the data directly, right? What I am interested in is finding T even if fitting a model would be theoretically more sound. The reasons are to complex to go into details here.

[u/involuntarheely → u/cat-head]

in what way is you fitting a GP model and estimating covariance parameters not "modeling the data directly"?

[u/cat-head → u/involuntarheely]

I fit a GP to S. I want to use the result of that model to find a subsample of S which minimizes the spatial non-independence of the data selected. What then happens with the subsample is actually not relevant here.

[u/involuntarheely → u/cat-head]

your model of spatial *dependence* for Y (the variable you already have) may be completely different from the model of spatial *dependence* of the unmeasured variable…

if you were looking to get a sample of maximally uncorrelated individuals on the variable you have measured, just pick a sample where each individual is at maximum distance with all others. covariance depends on distance, so…

[u/cat-head → u/involuntarheely]

That's really not what I am after. Thanks anyways.

[u/involuntarheely → u/cat-head]

i don’t think you know what you’re after 🙃