In this paper, we consider the meta learning problem for estimating the graphs associated with high-dimensional Ising models, using the method of $\ell_1$-regularized logistic regression for neighborhood selection of each node. Our goal is to use the information learned from the auxiliary tasks in the learning of the novel task to reduce its sufficient sample complexity. To this end, we propose a novel generative model as well as an improper estimation method. In our setting, all the tasks are \emph{similar} in their \emph{random} model parameters and supports. By pooling all the samples from the auxiliary tasks to \emph{improperly} estimate a single parameter vector, we can recover the true support union, assumed small in size, with a high probability with a sufficient sample complexity of $\Omega(1) $ per task, for $K = \Omega(d^3 \log p ) $ tasks of Ising models with $p$ nodes and a maximum neighborhood size $d$. Then, with the support for the novel task restricted to the estimated support union, we prove that consistent neighborhood selection for the novel task can be obtained with a reduced sufficient sample complexity of $\Omega(d^3 \log d)$.

翻译：在本文中,我们考虑估算与高维Ising模型相关的图表的元学习问题, 使用 $@ ell_ 1$_ 1$- 正规化后勤回归法的方法来估算每个节点的邻居选择。 我们的目标是在学习新任务时使用从辅助任务中学到的信息来降低其足够的样本复杂性。 为此, 我们提出一个新的基因化模型以及不适当的估计方法。 在我们的设置中, 所有任务都是 \ emph{ prom} 模型参数和支持中的 \ emph{ random} 。 通过将辅助任务的所有样本集中到 emph{ improply} 估计一个单一参数矢量, 我们就可以恢复真正的支持联盟, 假设规模小, 且每个任务都具有相当的样本复杂性 $\ Omega(1) 美元 。 为此, 我们提议了一个全新的任务, $ = \ Om = = = = $nlog p) 任务 $ 的Ising 模型任务, $ p$ndes and ad ad frequestal sublectional exgration expliclection 。