论文标题
纳什有条件独立曲线
Nash conditional independence curve
论文作者
论文摘要
我们研究了Spohn条件独立性（CI）品种$ n $ - 玩家游戏的$ C_X $ $ x $，用于$ n $二进制二进制随机变量的无向图形模型，由一个边缘组成。对于通用游戏，我们表明$ C_X $是Segre Variety $（\ Mathbb {p}^{1}^{1}）^{n-2} \ times \ times \ times \ Mathbb {p}^3 $ and explicit Formula的表格和Genus的典范。我们证明了两个通用定理，用于$ c_x $：任何具有真实行的Aggine真实代数品种的产品或任何$ \ Mathbb {r}^m $中的任何仿射真实代数品种，最多最多由$ M-1 $ $ $ polynomials定义为$ C_X $ $ c_x $ for $ x $ x $ x $ x $ x $ x $ x $ x $。
We study the Spohn conditional independence (CI) variety $C_X$ of an $n$-player game $X$ for undirected graphical models on $n$ binary random variables consisting of one edge. For a generic game, we show that $C_X$ is a smooth irreducible complete intersection curve (Nash conditional independence curve) in the Segre variety $(\mathbb{P}^{1})^{n-2} \times \mathbb{P}^3$ and we give an explicit formula for its degree and genus. We prove two universality theorems for $C_X$: The product of any affine real algebraic variety with the real line or any affine real algebraic variety in $\mathbb{R}^m$ defined by at most $m-1$ polynomials is isomorphic to an affine open subset of $C_X$ for some game $X$.
