For X (your test data) and Y (your training data), we have our prior: X ~ N(0, <kernel>) and Y ~ N(<training values>, <identity>). For the joint distribution I

For X (your test data) and Y (your training data), we have our prior: X ~ N(0, <kernel>) and Y ~ N(<training values>, <identity>). For the joint distribution I can accept that the covariance will have the same kernel function (albeit on |X| + |Y| dimensions) but what would the mean be?