Weighted least-squares approximation with determinantal point processes and generalized volume sampling. (arXiv:2312.14057v2 [math.NA] UPDATED)

We consider the problem of approximating a function from $L^2$ by an element
of a given $m$-dimensional space $V_m$, associated with some feature map
$\varphi$, using evaluations of the function at random points $x_1,\dots,x_n$.
After recalling some results on optimal weighted least-squares using
independent and identically distributed points, we consider weighted
least-squares using projection determinantal point processes (DPP) or volume
sampling. These distributions introduce dependence between the points that
promotes diversity in the selected features $\varphi(x_i)$. We first provide a …

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