We study transfer learning for estimation in latent variable network models.
In our setting, the conditional edge probability matrices given the latent
variables are represented by $P$ for the source and $Q$ for the target. We wish
to estimate $Q$ given two kinds of data: (1) edge data from a subgraph induced
by an $o(1)$ fraction of the nodes of $Q$, and (2) edge data from all of $P$.
If the source $P$ has no relation to the target $Q$, the estimation error must
be $\Omega(1)$. However, we show that if the latent variables are shared, then
vanishing error is possible. We give an efficient algorithm that utilizes the
ordering of a suitably defined graph distance. Our algorithm achieves $o(1)$
error and does not assume a parametric form on the source or target networks.
Next, for the specific case of Stochastic Block Models we prove a minimax lower
bound and show that a simple algorithm achieves this rate. Finally, we
empirically demonstrate our algorithm's use on real-world and simulated graph
transfer problems.

我们研究潜在变量网络模型中的迁移学习。我们提出了一种利用图距离排序的高效算法，用于估计给定潜在变量的边缘概率矩阵 $P$ 和 $Q$，并在没有假设源网络和目标网络参数形式的情况下实现了 $o (1)$ 的估计误差，并在随机块模型中证明了极小化下界和一个简单算法的性能。最后，我们在真实世界和模拟图迁移问题上对我们的算法进行了实证验证。

潜变量网络模型的迁移学习

Transfer Learning for Latent Variable Network Models

This paper explores the field of semi-supervised Fr\'echet regression, driven
by the significant costs associated with obtaining non-Euclidean labels.
Methodologically, we propose two novel methods: semi-supervised NW Fr\'echet
regression and semi-supervised kNN Fr\'echet regression, both based on graph
distance acquired from all feature instances. These methods extend the scope of
existing semi-supervised Euclidean regression methods. We establish their
convergence rates with limited labeled data and large amounts of unlabeled
data, taking into account the low-dimensional manifold structure of the feature
space. Through comprehensive simulations across diverse settings and
applications to real data, we demonstrate the superior performance of our
methods over their supervised counterparts. This study addresses existing
research gaps and paves the way for further exploration and advancements in the
field of semi-supervised Fr\'echet regression.

本文探讨半监督的 Fréchet 回归领域，提出了两种基于图距离的半监督 NW Fréchet 回归和半监督 kNN Fréchet 回归方法，扩展了现有的半监督欧几里得回归方法的范围，并确定了它们在有限有标签数据和大量无标签数据的情况下的收敛速度，并考虑了特征空间的低维流形结构。通过广泛的模拟和对真实数据的应用，我们证明了我们的方法在性能上优于自身的有监督对照方法，填补了现有研究的空白，并为半监督的 Fréchet 回归领域的进一步探索和发展铺平了道路。