论文标题
在密集的常规图上的模型
Ising Models on Dense Regular Graphs
论文作者
论文摘要
在本文中，我们在密集的常规图上得出了一个参数ising模型的实验极限。特别是，我们表明，有限的实验是高温方面的高斯，在临界机构中无高斯，而在高温方向上是无限的高斯人的收集。我们还得出了最大似然和最大伪样估计量的限制分布，并研究了针对连续替代方案的假设测试的限制能力（在整个方案之间的缩放变化）。据我们所知，这是建立ISING模型实验的经典限制（更普遍的是Markov随机字段）的首次尝试。
In this paper, we derive the limit of experiments for one parameter Ising models on dense regular graphs. In particular, we show that the limiting experiment is Gaussian in the low temperature regime, non Gaussian in the critical regime, and an infinite collection of Gaussians in the high temperature regime. We also derive the limiting distributions of the maximum likelihood and maximum pseudo-likelihood estimators, and study limiting power for tests of hypothesis against contiguous alternatives (whose scaling changes across the regimes). To the best of our knowledge, this is the first attempt at establishing the classical limits of experiments for Ising models (and more generally, Markov random fields).
