I was reading this link over here: https://peterroelants.github.io/posts/gaussian-process-tutorial/ . I came across the following statements:
I am trying to understand how to "fill in the entries" of the vector [mu_1,mu_2].
Based on the context, we can see that "mu_1" and "mu_2" are not scalars - we can see that "mu_1" and "mu_2" are both vectors themselves.
Suppose I have the following data:
- Fully Known: (x1,y1), (x2, y2) .... (xn,yn)
- Partially Known: (x_n+1), (x_n+2) .... (x_n+m)
In this case, I am interested in knowing how to "fill in the entries" of the [mu_1, mu_2] vector. In theory, would the [mu_1, mu_2] vector look like : [mu_1, mu_2] = [m(x1), m(x2) .... m(xn), m(x_n+1), m(x_n+2) ....m(x_n+m)] ?
My Question: In the case of the [mu_1, mu_2] vector, can we simply "stack" all these elements on top of each other? Is there such a thing as a "stacked vector notation" in mathematics?
Thanks!
Note: I think in the real world, when we are trying to find the joint probability distribution of [y1, y2] - I am not sure how to calculate m(X2) . In Gaussian Processes, I am told that mu_1 = m(X1) = m(Y1) . I do not know how we could calculate mu_2 = m(X2) = m(Y2) since Y2 is unknown in real world applications.