Data Science Asked by J.Galt on June 17, 2021
Assume that I have a set of $N$ points $x_i, i=1,…,N,$ in some space $mathbb{R}^D$, and corresponding point-wise (scalar) function evaluations $f(x_i)$. It is my goal to approximate the unknown function $f(x)$ with RBF kernels:
$$tilde{f}(x)=sum_{i=1}^N w_i k(x,x_i)$$
where $k(x,x_i)$ is a RBF kernel centred on $x_i$. It may seem intuitive to set $w_i=f(x_i)$, but then I will usually not reclaim $f(x_i)$ due to the influence of other basis functions. Towards this end, I have a number of questions, and would appreciate it if you could answer some of them:
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