The goal of Causal Discovery is to find automated search methods for learning
causal structures from observational data. In some cases all variables of the
interested causal mechanism are measured, and the task is to predict the
effects one measured variable has on another. In contrast, sometimes the
variables of primary interest are not directly observable but instead inferred
from their manifestations in the data. These are referred to as latent
variables. One commonly known example is the psychological construct of
intelligence, which cannot directly measured so researchers try to assess
through various indicators such as IQ tests. In this case, casual discovery
algorithms can uncover underlying patterns and structures to reveal the causal
connections between the latent variables and between the latent and observed
variables. This thesis focuses on two questions in causal discovery: providing
an alternative definition of k-Triangle Faithfulness that (i) is weaker than
strong faithfulness when applied to the Gaussian family of distributions, (ii)
can be applied to non-Gaussian families of distributions, and (iii) under the
assumption that the modified version of Strong Faithfulness holds, can be used
to show the uniform consistency of a modified causal discovery algorithm;
relaxing the sufficiency assumption to learn causal structures with latent
variables. Given the importance of inferring cause-and-effect relationships for
understanding and forecasting complex systems, the work in this thesis of
relaxing various simplification assumptions is expected to extend the causal
discovery method to be applicable in a wider range with diversified causal
mechanism and statistical phenomena.

寻找自动化搜索方法，从观察数据中学习因果结构；讨论潜变量和观察变量之间的因果联系以及它们之间的潜在模式和结构；提出了不同于高斯分布条件的 k - 三角性忠诚度的另一定义，可用于非高斯分布；轻松学习具有潜变量的因果结构的充分性假设。

因果结构学习中的非线性、反馈与一致性

Nonlinearity, Feedback and Uniform Consistency in Causal Structural  Learning

We consider distributed parameter estimation using interactive protocols
subject to local information constraints such as bandwidth limitations, local
differential privacy, and restricted measurements. We provide a unified
framework enabling us to derive a variety of (tight) minimax lower bounds for
different parametric families of distributions, both continuous and discrete,
under any $\ell_p$ loss. Our lower bound framework is versatile and yields
"plug-and-play" bounds that are widely applicable to a large range of
estimation problems, and, for the prototypical case of the Gaussian family,
circumvents limitations of previous techniques. In particular, our approach
recovers bounds obtained using data processing inequalities and Cram\'er--Rao
bounds, two other alternative approaches for proving lower bounds in our
setting of interest. Further, for the families considered, we complement our
lower bounds with matching upper bounds.

本文提出了一种统一的框架，用于基于交互式协议的分布式参数估计，可以导出各种紧密下限，适用于不同的参数分布族；特别是在高斯家族的原型情况下，我们的方法可以规避以往技术的局限性，并补充了匹配的上限。