论文标题
在一般凸度条件下，功能价值受限，并应用于分布式仿真
Constrained Functional Value under General Convexity Conditions with Applications to Distributed Simulation
论文作者
论文摘要
我们显示了满足一般凸度条件的密度约束功能值的一般现象，这概括了Bobkov and Madiman（2011）的观察值，即在对数 - 腔符号随机矢量中的每个维度中的每个坐标的熵在任何维度上与给定密度的任何维度的距离范围为1。 $ i_ϕ（f）= \ int _ {\ mathbb {r}^n} ϕ（f（x））dx $，假设$ψ^{ - 1}（f（x））$的凸度，并确定在大多数示例中满足这些范围的这些范围的紧密度。我们将此结果应用于连续的随机变量的分布式模拟，并建立了$β$ - concave关节密度的确切常见信息的上限，这是对Li and El Gamal（2017）中对数凸透密度的概括。
We show a general phenomenon of the constrained functional value for densities satisfying general convexity conditions, which generalizes the observation in Bobkov and Madiman (2011) that the entropy per coordinate in a log-concave random vector in any dimension with given density at the mode has a range of just 1. Specifically, for general functions $ϕ$ and $ψ$, we derive upper and lower bounds of density functionals taking the form $I_ϕ(f) = \int_{\mathbb{R}^n} ϕ(f(x))dx$ assuming the convexity of $ψ^{-1}(f(x))$ for the density, and establish the tightness of these bounds under mild conditions satisfied by most examples. We apply this result to the distributed simulation of continuous random variables, and establish an upper bound of the exact common information for $β$-concave joint densities, which is a generalization of the log-concave densities in Li and El Gamal (2017).
