Tree density estimation. (arXiv:2111.11971v5 [math.ST] UPDATED)

We study the problem of estimating the density $f(\boldsymbol x)$ of a random
vector ${\boldsymbol X}$ in $\mathbb R^d$. For a spanning tree $T$ defined on
the vertex set $\{1,\dots ,d\}$, the tree density $f_{T}$ is a product of
bivariate conditional densities. An optimal spanning tree minimizes the
Kullback-Leibler divergence between $f$ and $f_{T}$. From i.i.d. data we
identify an optimal tree $T^*$ and efficiently construct a tree density
estimate $f_n$ such that, without any regularity conditions on the density …

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