Maximum-likelihood degree formula for generic polygon Wachspress models

From papers

Let AR0(n2)×nA \in \mathbb{R}^{(n-2) \times n}_{\geq 0} be generic among matrices having a cell whose fibers are nn-gons. Let CCmaxC \subset C_{\max} be a cell, choose bint(C)b \in \operatorname{int}(C), let PbP_b be the corresponding fiber, and set Q=BTPbQ=B^T \cdot P_b. Denote by MC(Q)M_{\mathbb{C}}(Q) the Wachspress model of QQ.

Wachspress ML-degree conjecture. For a generic nn-gon QQ, the maximum likelihood degree is

MLdeg(MC(Q))=(n1)(n2)+(n3)(n5)1.\operatorname{MLdeg}(M_{\mathbb{C}}(Q))=(n-1)(n-2)+(n-3)(n-5)-1.

The conjecture gives the predicted maximum likelihood degree for generic polygonal Wachspress models. The paper presents it as an expected formula and does not establish it unconditionally.

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Sources & referencesView supporting material

Primary source

Dmitrii Pavlov and Simon Telen, “Santaló Geometry of Convex Polytopes”, arXiv:2402.18955 (2024).

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